When you stomp, you thud your feet down heavily as you walk. An angry teenager might stomp down the hall and slam the door to his room.
A little boy in big cowboy boots might stomp around the house enjoying the sound of his heels against the floor, and an awkward marching band could stomp heavily down the street playing the theme from "Rocky." You can also use the word stomp to describe a specific kind of stamping dance. This meaning has been around since about 1912, from popular jazz slang. The earlier stomp was simply a variation on the word stamp.