Dig-Darsini-Tika by Srila Sanatana Gosvami:
Now, by the potency of prayer, feelings of spontaneous love arise and one especially craves to have the direct vision of the Lord. In this regard, when referring to topics about saksat-darsana or direct vision of the Lord, only sri nama-sankirtana is the parama sadhana or supreme method for this attainment. After fixing His beauty in the mind, one then offers sorrowful prayers by way of sri nama-kirtana, as in this verse beginning with namo. In the text of a mula-sloka such as this sixth verse, usually the word tubhyam ("unto You") would be found in order to complete the sense of the prayer; but in this case, the excitement of prema causes the reciter to neglect all feelings of awe or reverence. Therefore, in the mood of being in the personal presence of the Lord, the word tubhyam is neglected.
He prabho - means he madiya isvara, O my controller! (Offering You my obeisances, I beg) prasida - this word indicates prasadam, or be pleased with me and show Your mercy. (The reason for praying is) I am duhkha-jalabdhi-magnam - immersed in the ocean of misery. Specifically, the word duhkha (pain, misery, distress) indicates either the agony of repeated birth and death in the samsarika material world, or else the torment of not seeing You (resulting in feelings of ocean-like infinite desolation). Jalam - (meaning net, illusion, deception), and abdhih (ocean) denotes the extreme vastness - (By the force of my own karma) I am thus magnam (submerged). (I am tortured by all these harsh afflictions); therefore I am ati-dinam - very distressed.
Or else, another meaning of the word ati-dinam is - I am completely bereft of the association of saintly persons, and consequently without their assistance I am extremely fallen. Or else, yet another meaning is - (due to not seeing You) I am just like a living dead man. In this regard, I am also ajnam - I am particularly ignorant about how to resolve this problem. Then krpaya drsti-vrstya - showing Your own mercy, please shower me with Your nectar-laden glances - anugrhana - thereby uplifting me and once more enthusing me with life. This alone is the purport of the prayer. Then aksi-drsyo-edhi - please become visible before my eyes.
Prayers are usually made according to the sequence in which this one is prayed; as such it is not appropriate in this case to first mention the boon that is being requested, due to its nature of being the topmost of rarely attained benedictions.
The glory of attaining the direct vision of the Lord (saksat-darsana) within the mind is explained very logically by the personal associates of the Lord (sri bhagavat parsada) in the Brhad Bhagavatamrta, Uttara Khanda 3.179-182 *please see Appendix C, page 27* from this passage one may gain specific knowledge of these topics.
(Now the devotional kirtana of the Lord's names, used to address Him at the beginning of the mula-sloka, will be explained:) In this sixth verse the word deva indicates he divya rupa - O Lord of divine beauty! This beauty is the cause for desiring His darsana. The address of damodara intimates specifically that He is glorified for His excellence of bhakta-vatsalya, or affection for His devotees (up to the point of allowing them to bind Him around the waist). Therefore I will be qualified only by bhakti to see Him with my own eyes. He Who has no end (Whose mercy has no limits) is addressed as ananta. Therefore He will certainly shower His glance of mercy and thus favour me. The address prabhu connotes he acintya-ananta-adbhuta-maha-sakti-yukta - O You Who are endowed with inconceivable, limitless, astonishingly grand potency! Therefore You Who cannot be perceived by the senses can only become visible to my eyes by dint of this same inconceivable sakti of Yours. Addressing Him as isa suggests - he parama-svatantra - O You Who are supremely independent! In showing Your favour even to unfit souls, You are dependent on no one else. And moreover, the address visnu means he sarva-vyapaka - O You Who are all-pervading! Furthermore, it means - O You Who are fond of entering into Vrndavana's secluded caves and bower-cottages! Praying like this indicates that it is not difficult for Him to come before one's eyes; He does not have to labour hard to come from a distance.
(Some additional interpretations of the above-mentioned forms of address are now given:) Or else, he ananta means that He is aparicchinna or continuously existent without interval or separation. The address of visnu means He is sarva-vyapin or living everywhere. Therefore, he damodara proclaims Him thus - under the sway of His own parama-vatsalya-visesa or supremely affectionate attribute, there is absolutely nothing that He cannot do. The purport of the other words used for addressing Him may also be understood in terms of these expanded indications.