Cows graze on grass, and people graze on snacks and finger foods. Graze can also mean to scrape, like when you graze your elbow after falling off your bike.
Graze means "to feed on grass" as sheep, horses, cows, do in a meadow — they eat a little at a time, but constantly. People sometimes graze too, munching on small snacks all day long instead of having a real meal. It also means “to touch lightly,” like when I pitch a baseball to you — and I accidentally hit your arm. With luck, the ball only grazed you, meaning you aren't hurt at all.