The most profound effect I noticed myself is learning passages of music on an instrument (note I'm an amateur, and not especially good!) After not too long trying to learn/practise one evening, I will be noticeably better the next day.
I've recently found that reading before going to sleep (while not staying up late reading) opens my mind the next day and I wake up knowing whether I have accepted or rejected a premise of a nonfiction book. It's like I read, don't think about it then, but then as I sleep I make up my mind or have more questions about the things that I read.
It's strange, and I wish I could learn more about this phenomenon.
The fiction thing is interesting.
The Dark Souls series of video games are known to be hard, especially the bosses. Many people, myself included, have experienced being stuck on a boss and after 20 attempts they give up for the night. Next time you start the game up you beat the boss on the first attempt!
It's hard to know if this is because your subconscious mind kept working on the problem, or if new neural pathways were formed to handle the eye-hand coordination, or, as you suggest, you just came back to the problem refreshed.
Being refreshed, and not frustrated and tired, seems like the simplest explanation for this.