A daydream is a fantasy you have while you're awake. Daydreams are pleasant, and they can be so absorbing that they distract you from what's going on around you.
You might have a daydream about moving to a big city, or about how you'd spend your millions if you won the lottery. To do this — dream, muse, or fantasize — is also to daydream. Your math teacher might scold you, saying, "You can't daydream in the middle of the calculus final!" The word dates from the 17th century.