The most significant expression in this verse is pārthivārbhakaḥ, son of the King. When Dhruva Mahārāja was at home, although he was a king's son, he was prevented from getting on the lap of his father. But when he became advanced in self-realization, or devotional service, by the pressure of his toe he could push down the whole earth. That is the difference between ordinary consciousness and Kṛṣṇa consciousness. In ordinary consciousness a king's son may be refused something even by his father, but when the same person becomes fully Kṛṣṇa conscious within his heart, he can push down the earth with the pressure of his toe.
One cannot argue, "How is it that Dhruva Mahārāja, who was prevented from getting up on the lap of his father, could press down the whole earth?" This argument is not very much appreciated by the learned, for it is an example of nagna-mātṛkā logic. By this logic one would think that because his mother in her childhood was naked, she should remain naked even when she is grown up. The stepmother of Dhruva Mahārāja might have been thinking in a similar way: since she had refused to allow him to get up on the lap of his father, how could Dhruva perform such wonderful activities as pressing down the whole earth? She must have been very surprised when she learned that Dhruva Mahārāja, by concentrating constantly on the Supreme Personality of Godhead within his heart, could press down the entire earth, like an elephant who presses down the boat on which it is loaded.