Imagine small animals like birds using their beaks for tiny, quick bites. 'Peck at' is similar. Chickens peck at grains, breaking them into pieces.
Pro Tip 2/3
Not Hungry
When someone is not very hungry or unsure about the food, they might just peck at their meal. She just pecked at her dinner, moving the food around her plate.
Pro Tip 3/3
Disinterest
Use 'peck at' to describe someone eating without enthusiasm or interest in the food. He pecked at his food while staring out the window.