The word calac-caraṇāravindam refers to the Supreme Personality of Godhead, who actually walks or travels upon the surface of the world. For example, Lord Rāmacandra actually walked on the surface of the world, and Lord Kṛṣṇa also walked just like an ordinary man. The prayer is therefore offered to the Supreme Personality of Godhead, who descends to the surface of this earth, or any part of this universe, for the protection of the pious and the destruction of the impious. It is confirmed in Bhagavad-gītā that when there is an increase of irreligion and discrepancies arise in the real religious activities, the Supreme Lord comes to protect the pious and kill the impious. This verse indicates Lord Kṛṣṇa.
Another significant point in this verse is that the Lord comes, icchayā, by His own will. As Kṛṣṇa confirms in Bhagavad-gītā, sambhavāmy ātma-māyayā: (BG 4.6) "I appear at My will, by My internal potential power." He is not forced to come by the laws of material nature. It is stated here, icchayā: He does not assume any form, as the impersonalists think, because He comes at His own will, and the form in which He descends is His eternal form. As the Supreme Lord puts the living entity into the condition of horrible existence, He can also deliver him, and therefore one should seek shelter at the lotus feet of Kṛṣṇa. Kṛṣṇa demands, "Give up everything and surrender unto Me." And it is also said in Bhagavad-gītā that anyone who approaches Him does not come back again to accept a form in material existence, but goes back to Godhead, back home, never to return.