Contrary to what his companions believe, the Doctor does sleep, he just does it when no one’s looking. Everybody needs sleep; it’s an unavoidable biological necessity, required for both psychological and physical heath. If you don’t sleep, you don’t dream, and dreams are important.
The Doctor’s seen so much in his travels. He dreams of many things, but most precious of all are his dreams of home. He sees Gallifrey as he remembers her best, the Citadel gleaming beneath its dome, the red grass and orange sky.
It’s so beautiful, so heartbreaking, that he wakes with tears in his eyes.