To chomp is to bite something in a greedy, noisy way. If you've got five minutes to eat breakfast, you might quickly chomp your bagel as you walk to catch the bus.
People who chomp their food are either extremely hungry or somewhat ill-mannered: watching someone chomp a hamburger and fries can make you lose your appetite. You can also use chomp as a noun, to mean "a great big bite," as when your brother grabs your slice of pizza and takes a chomp. The word has been used in American English since the mid-1600s, from the earlier verb champ.