Whenever I'm learning something new on the piano, I'll usually
- learn the basic notes and rhythm of a section of the song (several measures, maybe a full page depending on the complexity / tempo, etc).
- Practice that section for a little while. Depending on the complexity / length of the section (once again), this could be around 30 - 90 minutes. Usually I do this in the evening, near the time when I'm going to sleep.
- At this point, even if it's a little sloppy, I stop for the night and go to bed.
9 times out of 10, I feel much more comfortable with that section when I play the piece the following day than I did when I stopped the night before - I seem to have improved over night. I no longer have that "rushed" feeling you sometimes get when you're trying hard to make sure you don't miss any notes; the section just flows much better.
I'm interested in hearing whether others have experienced this (I'm thinking so based on the last sentence in this answer by @Kyle Brandt) and, if so, what is this phenomenon (e.g. is there a name for it, what causes it, etc.)?