Lord Śrī Caitanya Mahāprabhu explained this ātmārāma śloka very vividly before His chief devotee Śrīla Sanātana Gosvāmī. He points out eleven factors in the śloka, namely (1) ātmārāma, (2) munayaḥ, (3) nirgrantha, (4) api, (5) ca, (6) urukrama, (7) kurvanti, (8) ahaitukīm, (9) bhaktim, (10) ittham-bhūta-guṇaḥ and (11) hariḥ. According to the Viśva-prakāśa Sanskrit dictionary, there are seven synonyms for the word ātmārāma, which are as follows: (1) Brahman (the Absolute Truth), (2) body, (3) mind, (4) endeavor, (5) endurance, (6) intelligence and (7) personal habits.
The word munayaḥ refers to (1) those who are thoughtful, (2) those who are grave and silent, (3) ascetics, (4) the persistent, (5) mendicants, (6) sages and (7) saints.
The word nirgrantha conveys these ideas: (1) one who is liberated from nescience, (2) one who has no connection with scriptural injunction, i.e., who is freed from the obligation of the rules and regulations mentioned in the revealed scriptures like ethics, Vedas, philosophy, psychology and metaphysics (in other words the fools, illiterate, urchins, etc., who have no connection with regulative principles), (3) a capitalist, and also (4) one who is penniless.
According to the Śabda-kośa dictionary, the affix ni is used in the sense of (1) certainty, (2) counting, (3) building, and (4) forbiddance, and the word grantha is used in the sense of wealth, thesis, vocabulary, etc.
The word urukrama means "the one whose activities are glorious." Krama means "step." This word urukrama specifically indicates the Lord's incarnation as Vāmana, who covered the whole universe by immeasurable steps. Lord Viṣṇu is powerful, and His activities are so glorious that He has created the spiritual world by His internal potency and the material world by His external potency. By His all-pervading features He is everywhere present as the Supreme Truth, and in His personal feature He is always present in His transcendental abode of Goloka Vṛndāvana, where He displays His transcendental pastimes in all variegatedness. His activities cannot be compared to anyone else's, and therefore the word urukrama is just applicable to Him only.
According to Sanskrit verbal arrangement, kurvanti refers to doing things for someone else. Therefore, it means that the ātmārāmas render devotional service unto the Lord not for personal interest but for the pleasure of the Lord, Urukrama.