Sri Gopala Guru Goswami has given a beautiful meaning of the Hare Krishna Mahamantra as below:
Hare Krishna Hare Krishna Krishna Krishna Hare Hare
Hare Rama Hare Rama Rama Rama Hare Hare
The Lord’s divine and intimate qualities as revealed in the Maha Mantra:
Meaning of “Hari”
hari harati papani dusta cittair api smrtah
anicchayapi samsprsto dahaty eva hi pavakah
“Just as the fire, on contacting an object, automatically burns it, so the name of Hari takes away (harati) or burns up all the sins of the people with materialistic hearts. It removes (harati) all ignorance and reveals the transcendental, blissful form of the Lord.“
vijnāpya bhagavat-tattvaṁ cid-ghanānanda-vigraham
haraty avidyāṁ tat-kāryam ato harir iti smṛtaḥ
The Lord is known as Hari, for he takes away the ignorance of His devotees by revealing to them both His actual nature as Supreme Lord and His personal spiritual form.
Meaning of “Hare”
harati kṛṣṇa-manaḥ kṛṣṇāhlāda-svarūpiṇī
ato harety anenaiva śrī-rādhā parikīrtitā
Because She steals Krishna’s mind and because She is the incarnation of Krishna’s joy, Radha is also known by the name Harā.
The word ‘hare’ has another meaning:
svarupa prema vatsalyair harer harati ya manah
hara sa kathyate sadbhih sri radha vrsabhanuja
Hara is Srimati Radhika, daughter of Vrsabhanu, who steals (harati) the mind of Hari, Krsna, by her unalloyed love. Hara, in the form of address, also becomes ‘hare’.
Meaning of “Krishna”
krsir bhu vacakah sabdo nas cananda svarupakah
tayor aikyam param brahma krsna ity abhidhiyate
“The word ‘krsna’ is composed of the root ‘krsi’ meaning ‘bhu,’ the shelter of all existence and the word ‘na’ meaning ‘nivriti’ or the form of supreme bliss. Combined they form the word ‘krsna’ which signifies the param brahma, the supreme personality of Godhead with blissful form.”
ānandaika-sukha-svāmī śyāmaḥ kamala-locanaḥ
gokulānandano nanda-nandanaḥ kṛṣṇa īryate
The son of Nanda, the dark, lotus-eyed lord, the only master of the highest joy who brings pleasure to Gokula is known as Krishna.
Meaning of “Rama”
ramante yogino’nante saty ānanda-cid-ātmani
iti rāma-padenāsau para-brahmābhidhīyate
Yogis take pleasure in the Supreme Self, which is existence, knowledge and bliss absolute. Therefore that truth, known as the Param Brahman is also called Rama. (Rāma-tāpanīyopaniṣad, 1.6)
vaidagdhya-sāra-sarvasvaṁ mūrti-līlādhidaivatam
śrī-rādhāṁ ramayan nityaṁ rāma ity abhidhīyate
Krishna is also known as Rama because the joys of conjugal life are the essence of His being, because He is the titulary deity of loving sports incarnate, and because He brings pleasure to Srimati Radharani.
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