A nook is a cozy little corner or a small, safe area. A nook in the library can be a nice place to sit and read.
If you have a "breakfast nook" in your kitchen, you know it's a space set back from the main room, maybe built into a corner or under a window, where you can sit at a small table. All nooks are small and sheltered in some way. You may have come across nook in the phrase "nook and cranny." This is often meant figuratively, as when you search every single nook and cranny in your whole house looking for your wallet.