I am reposting this translation by Jagat from the Daily Meditations - section to have it better available for everyone in the future.
As part of Harinama-chintamani, we will be including a fairly substantial appendix with many Maha Mantra vyakhyas. Here is one attributed to Jiva Goswami.
MahA-mantrArtha-vyAkhyA
hare kRSNa hare kRSNa kRSNa kRSNa hare hare |
hare rAma hare rAma rAma rAma hare hare ||(1)
sarva-ceta-haraH kRSNas tasya cittaM haraty asau |
vaidagdhI-sAra-vistArair ato rAdhA harA matA ||
Krishna steals everyone’s mind, but Radharani steals even His when She makes use of Her divine talents. Therefore She is known as HarA.
(2)
karSati svIya-lAvaNya-muralI-kala-niHsvanaiH |
zrI-rAdhAM mohana-guNAlaGkRtaH kRSNa Iryate ||
Because He forcibly pulls Radha from Her home with the sound of His flute filled with His loveliness, that Lord of all enchanting virtues is known as Krishna.
(3)
zrüyate nIyate rAse hariNA hariNekSaNA
ekAkinI rahaH-kuJje hareyaM tena kathyate ||
It is heard that doe-eyed Radha was taken by Krishna during the Rasa dance to spend time with Him alone in a secret grove in the forest. She is therefore known as HarA.
(4)
aGga-zyAmalima-stomaiH zyAmalIkRta-kAJcanaH |
ramate rAdhayA sArdhaM kRSNo nigadyate ||
The black effulgence of Krishna’s body turns even the gold of Radharani’s skin to black when He embraces Her. He is thus known as Krishna.
(5)
kRtvAraNye saraH-zreSThaM kAntayAnumatas tayA |
AkRSya sarva-tIrthAni taj-jJAnAt kRSNa Iryate ||
When Radharani ordered Krishna to build the most beautiful water tank in the world (as a penance for killing Arishtasura), He called all the holy rivers and tanks to bring water to fill it. Thus He is known as Krishna.
(6)
kRSyate rAdhayA premNA yamunA-taTa-kAnanam |
lIlayA lalitaz cApi dhIraiH kRSNa udAhRtaH ||
Because He is forcibly attracted into the forests on the Yamuna’s banks by Radha’s ecstatic love, where He becomes Her playful lover, He is known by the wise as Krishna.
(7)
hRtavAn gokule tiSThann ariSTaM puSTa-puGgavam |
zrI-haris taM rasAd uccai rAyatIti harA matA ||
While living in Gokula, Krishna destroyed the powerful demon known as Arishta. At that time, Radha called out to Him with great emotion. Doing so, she stole His mind and so is known as HarA.
(8)
hy asphuTaM rAyati prIti-bhareNa hari-ceSTitam |
gAyatIti matA dhIrair harA rasa-vicakSaNaiH ||
Filled with sweet affection, Radha sometimes glorifies Krishna’s pastimes quietly, and sometimes She sings them aloud. Thus those who know the secrets of divine rasa call Her HarA.
(9)
rasAveza-parisrastAM jahAra muralIM hareH |
hareti kIrtitA devI vipine keli-lampaTA ||
Sometimes Krishna becomes so absorbed in Radha’s love that His beloved flute slips from His hand. Mad with the desire to enjoy pastimes in the forest bowers with Krishna, Radha steals Krishna’s flute. That goddess is thus known as HarA.
(10)
govardhana-darI-kuJje parirambha-vicakSaNaH |
zrI-rAdhAM ramayAmAsa rAmas tena mato hariH ||
When Krishna, the expert embracer, makes love with Radha in the forest bowers or the
caves of Govardhan, He is known as Rama.
(11)
hanti duHkhAni bhaktAnAM rAti saukhyAni cAnvaham |
harA devI nigaditA mahA-kAruNya-zAlinI ||
Radha most compassionately destroys the miseries of Her devotees and gives them great joy every single day. Therefore she is known as HarA.
(12)
ramate bhajato cetaH paramAnanda-vAridhau |
atreti kathito rAmaH zyAmasundara-vigrahaH ||
Krishna, with His beautiful blackish form, submerges the minds of those who worship Him in an ocean of supreme bliss. Therefore He is known by the name Rama.
(13)
ramayaty acyutaM premNA nikuJja-vana-mandire |
rAmA nigaditA rAdhA rAmo yutas tayA punaH ||
In a temple forest groves, Radharani brings the infallible Krishna to the pinnacle of joy with Her love. Therefore She is called RAmA. Since Krishna is always by Her side, He is known as Rama.
(14)
rodanair gokule dAvAnalam azayati hy asau |
vizoSayati tenokto rAmo bhakta-sukhAvahaH ||
When Krishna heard the cries of the Vrajavasis, who were afraid of the forest fire, He quickly swallowed it up, drying their tears. By giving them joy in this way, He is known as Rama.
(15)
nihantum asurAn yAto mathurA-puram ity asau |
tadAgamad rahaH-kAmo yasyAH sA’sau hareti ca ||
Krishna left Vraja for Mathura in order to slay the demons, but later returned, drawn by the desire to be alone with Radha. Because She attracted Him back to Vraja, She is known as HarA.
(16)
Agatya duHkha-hartA yo sarveSAM vraja-vAsinAm |
zrI-rAdhA-hAri-carito hariH zrI-nanda-nandanaH ||
When the son of Nanda returned to Vraja after many years in Mathura and Dvaraka, He took away all the distress of its residents. His every action steals the heart of Srimati Radharani, and so He is known as Hari.
I just discovered Jagadananda's translation of Gopal Guru Gosvami's explanation of the Maha-mantra from the internet. I'll post it here to accompany Jiva's vyAkhya.
EXPLANATION OF THE MAHA-MANTRA
by Gopala Guru Gosvami
Translated by Jagadananda Dasa
(1)
hare - he hare, mac-cittam hrtva bhava-bandhanan mocaya |
Hare! O Hari, steal my mind and deliver me from bondage to this material world.
krsna - he krsna, mac-cittam akarsaya |
Krsna! O Krsna, attract my mind.
hare - he hare, sva-madhuryena mac-cittah hara |
Hare! O Hari! Capture my mind with the sweetness of your name, form and pastimes.
krsna - he krsna, sva-bhakta-dvara bhajana-jnana-danena mac-cittam sodhaya |
Krsna! O Krsna! Send me the association of your devotees who will purify my mind through instructions about your devotional service.
krsna - he krsna, nama-rupa-guna-liladisu man-nistham kuru |
Krsna! O Krsna! Give me unflinching faith in your name, form, qualities and pastimes.
krsna - he krsna, rucir bhavatu me |
Krsna! O Krsna! Give me a taste for your name, form, qualities and pastimes.
hare - he hare, nija-seva-yogyam mam kuru |
Hare! O Hari! Make me worthy to engage in your service.
hare - he hare, sva-sevam adisaya |
Hare! O Hara, Radha! Order me personally in the service you wish me to perform.
hare - he hare, sva-presthena saha svabhista-lilam sravaya |
Hare! O Hara, Radha! Give me the opportunity to hear about your own favorite pastimes with your beloved Lord.
rama - he rama, presthaya saha svabhista-lilam mam sravaya |
Rama! O Rama! Give me the opportunity to hear about your own favorite pastimes with your beloved Radha.
hare - he hare, sva-presthena saha svabhista-lilam darsaya |
Hare! O Hara, Radha! Give me the opportunity to see your intimate pastimes with your beloved Lord.
rama - he rama, presthaya saha svabhista-lilam mam darsaya |
Rama! O Rama! Give me the opportunity to see your intimate pastimes with your beloved Radha.
rama - he rama, nama-rupa-guna-lila-smaranadisu mam yojaya |
Rama! O Rama! Engage me in hearing, chanting and remembering your name, form, qualities, pastimes.
rama - he rama, tatra mam nija-seva-yogyam kuru |
Rama! O Rama! As I enter into those pastimes by the path of meditation, make me worthy to engage in your service.
hare - he hare, mam svangikrtya ramasva |
Hare! O Hari! Please accept me and take pleasure from the service that I offer you.
hare - he hare, maya saha ramasva |
Hare! O Hari! Take pleasure in me and enjoy with me.
(2)
hare - krsnasya mano haratiti hara radha, tasyah sambodhane he hare |
Hare! Radha is known as Hara because she steals Krsna's mind. I call out to her, O Hare! O Radhe!
krsna - radhaya manah karsatiti krsnah, tasya sambodhane he krsna |
Krsna! The Lord is known as Krsna because he attracts Radha's mind. Therefore I call out to him, O Lord! O Krsna!
hare - krsnasya lokalajjadhairyadi sarvam haratiti hara radha, tasyah sambodhane he hare |
Hare! Radha steals Krsna's sense of public shame and his self-possession. She steals everything of his and is thus known as Hara. I therefore call out to her, O Radhe! O Hare!
krsna - radhaya lokalajjadhairyadi sarvam karsatiti krsnah, tasya sambodhane he krsna |
Krsna! He drags away all of Radha's sense of shame and her self-possession. Therefore I call out to him, O Lord! O Krsna!
krsna - yatra yatra radha tisthati gacchati va tatra tatra sa pasyati krsno mam sprsati balat kancukadikam sarvam karsati haratiti krsnah, tasya sambodhane he krsna |
Krsna! Wherever Radha is standing, or wherever she happens to be going, she thinks, Krsna is watching me, he is touching me, he he is pulling on my bodice. He is pulling on me. I call out to him, O Lord! O Krsna!
krsna - punar harsatam gamayati vanam karsatiti krsnah, tasya sambodhane he krsna |
Krsna! Then Krsna makes her feel a thrill of excitement as he pulls her to the woods. I call out to him, O Lord! O Krsna!
hare - yatra krsno gacchati tisthati va tatra tatra pasyati radha mamagre parsve sarvatra tisthatiti hara, tasyah sambodhane he hare |
Hare! Wherever Krsna goes, wherever he is situated, he sees Radha in front of him, by his side, all around him. In this way she disturbs his mind. I call out to her, O Radhe. O Hare!
hare - punas tam krsnam harati sva-sthanam abhisarayatiti hara radha, tasyah sambodhane he hare |
Hare! She once again steals Krsna away, making him come to her kunja. She is thus known as Hara. I thus call out to her, O Radhe! O Hare!
hare - krsnam vanam harati vanam agamayatiti hara radha, tasyah sambodhane he hare |
Hare! She once again steals Krsna away, making him come to her kunja. She is thus known as Hara. I thus call out to her, O Radhe! O Hare!
rama - ramayati tam narma-niriksanadiniti ramah, tasya sambodhane he rama |
Rama! Krsna is known as Rama because he brings Radha pleasure with his joking words and his loving glances. I thus call out to him, O Krsna! O Rama!
hare - tatkalikam dhairyavalambanadikam krsnasya haratiti hara radha, tasyah sambodhane he hare |
Hare! She robs Krsna of the momentary self-control he is able to muster in her presence. She is thus known as Hara, and so I call out to her, O Radhe! O Hare!
rama - cumbana-stana-karsanalinganadibhi ramate iti ramah, tasya sambodhane he rama |
Rama! Krsna delights in kissing Radha, in touching her breasts and in embracing her. He is thus known as Rama, and so I call out to him, O Lord! O Rama!
rama - punas tam purusocitam krtva ramayatiti ramah, tasya sambodhane he rama |
Rama! Krsna causes Radha to reach the pinnacle of sexual excitement, so that she becomes aggressively active in the love battle, like a man. He is thus known as Rama, and so I call out to him, O Lord! O Rama!
rama - punas tatra ramate iti ramah, tasya sambodhane he rama |
Rama! All this brings extra delight to Krsna. He is thus known as Rama, and so I call out to him, O Lord! O Rama!
hare - punah rasante krsnasya mano hrtva gacchatiti hara radha, tasyah sambodhane he hare |
Hare! Once again, at the end of the Rasa dance, as she leaves to return home, she steals Krsna's mind and takes it away with her. She is thus known as Hara, and I therefore call out to her, O Radhe! O Hare!
hare - radhaya mano hrtva gacchatiti harih krsnah tasya sambodhane he hare |
Hare! Krsna also steals Radha's mind, taking it with him as he leaves. He is thus known as Hari, and I call out to him, O Krsna! O Hare!
Now that I'm at it, here's Raghunatha Das Gosvami's Sri Harinamartha-ratna-dipika, also translated by Jagadananda.
Sri Harinamartha-ratna-dipika
by Raghunatha dasa Gosvami
translated by Jagadananda das
ekada krsna-virahad dhyayanti priya-sangamam |
mano-baspa-nirasartham jalpatidam muhur muhuh ||
hare krsna hare krsna krsna krsna hare hare |
hare rama hare rama rama rama hare hare ||
One day, Radha was feeling separation from Krsna and was meditating on the reunion she hoped to have with him. In order to rid herself of the depression she felt in his absence, she began to repeatedly chant his names. hare krsna hare krsna krsna krsna hare hare, hare rama hare rama rama rama hare hare.
he hare sva-madhuryena mac-ceto harasi |
O Hare! You steal my mind with your sweetness.
tatra hetur he krsna iti krs-sabdasya sarvarthah nas ca ananda-svarupa iti svarthe nah sac-cid-ananda-svarupaka iti sviyena sarva-dik-paramanandena sarvadhika-paramanandena va pralobhyeti bhavah |
With her next utterance of the name Krsna, she explains how that is possible. The name Krsna comes from the combination of the syllables krs, which means everything, and na, which means an identity steeped in bliss. Thus Krsna is the form of eternity, knowledge and bliss who attracts and tempts everyone in every direction with the supreme joy of his own being, a joy which is superior to any other.
tatas ca he hare dhairya-lajja-guru-bhayadikam api harasi ||
So, Hari, you take away even my most strongly held character traits, like self-control, shame, and fear of my superiors.
tatas ca he krsna sva-grhebhyo vanam prati mam akarsasi ||
Then, Krsna, you draw us out of our houses and into the forest.
tatas ca he krsna vanam pravistaya me kancukim sahasaivagatya karsasi ||
Then, when I have entered the woods, you suddenly appear out of nowhere and start pulling on my blouse.
tatas ca he krsna mat-kucau karsasi ||
Then, Krsna, you start touching my breasts.
tatas ca he hare sva-bahu-nibaddham mam puspa-sayyam prati harasi
Then, O Hari, you wrap me in your arms and lead me off to the bed of flower petals.
tatas ca he hare tatra nivesitaya me antariyam api baladd harasi ||
Then, O Hari, while I am sitting there helplessly, you tear off my skirt as well.
tatas ca he hare antariya-vasana-harana-misenatma-viraha-pidam sarvam eva harasi ||
And so, O Hari, by taking my clothes off my body, you take away all the sufferings accumulated in my soul as a result of my separation from you.
tatas ca he rama svacchandam mayi ramase ||
Then, O Rama, you enjoy with me to your full satisfaction.
tatas ca he hare yad avasistam kincin me vamyam asit tad api harasi ||
By so doing, O Hari, whatever little recalcitrance was left in me, that too was stolen by you.
tatas ca he rama mam ramayasi svasmin purusayitam api karosi ||
And so, O Rama, I become so frenzied with passion that I take the initiative in lovemaking, like a man.
tatas ca he rama ramaniya-cudamane tava navina-vaktra-madhuryam api nihsankam tad atmanam tava ramaniyakam man-nayanabhyam dvabhyam evasvadyate iti bhavah ||
Then, O Rama, you who are the crest-jewel of the charming! Without any interference, I can now relish the beauty of your youthful face, indeed the very beauty of your very soul with both of my eyes.
tatas ca he rama na kevalam ramana-rupenapi ramana-kartr-ramana-prayojakah |
kintu tad-bhava-rupa rati-murtir iva tvam bhavasiti bhavah ||
Then, O Rama, not only do you engage me in lovemaking by actively taking the role of a lover, even though this is true. It is as though you were also incarnate in the very act of love itself as its essence.
tatas ca he hare mac-cetana-mrgim api harasi, ananda-murccham prapayasiti bhavah ||
Then, O Hari, you who are like a lion, capture the deer of my mind. In other words, your loving makes me faint.
yato he hare simha-svarupa tad api rati-karmani prakatita-maha-pragalbhya iti bhavah ||
Because you are a lion, O Hari, you have shown such self-confidence, proficiency and boldness in the art of love.
evambhutena tvaya preyasa viyukta ksanam api kalpa-kotim iva katham yapayitum prabhavamiti svayam eva vicaraya iti nama-sodasakasyabhiprayah | tatas ca namabhis cumbakair iva krsnah krsnaya sahasaivakrsto milita-paramananda eva | tasyah sva-sakhinam tat-parivara-vargasya tad-bhava-sadhakanam arvacinanam api sri-radha-krsnau manasam sampurayatah ||
Being separated from you, my dearest lover, it seems that even a moment is like a million millennia. How then will I be able to suffer through this age-long separation? Please consider this fact. This is the summary meaning of the sixteen names of the Mahamantra. Having chanted them in this spirit, Krsna is attracted by Radha's chanting of these magnet-like names and he suddently appears to experience the ecstasy of union. May the Divine Couple, Sri Sri Radha-Krsna fulfill the desires of her sakhis, his cowherd friends, as well as of all those who today are engaged in the practices of devotional service in the hope of one day attaining the same mood of love.