Uddâlaka Âruni said to his son Svetaketu: 'Learn from me the true nature of sleep (svapna). When a man sleeps here, then, my dear son, he becomes united with the True, he is gone to his own (Self). Therefore they say, svapiti, he sleeps, because he is gone (apîta) to his own (sva).

In plain words: Uddalaka Aruni teaches his son what deep sleep really is. When a person sleeps deeply, he is joined with the True, the real Being, and goes back to his own Self. That is why the word for sleeping, svapiti, means 'gone to one's own.'