Some kind of food or drink that looks cute or delicious. It can also mean a comfort food (if the person using the word is sad).
The word is a kawaii term and is derived from the phrase "nom nom nom".
"I feel like getting nom noms... you in?"
"Sure! I know a great pastry shop! They have the cutest cupcakes!"
"Oh wow! That Mickey Mouse waffle looks nom nom! Waiter may I get one?"
"Can I please heave my nom nom...?"
"Sure! I'll go get you some pizza! It's your favorite!"