A stomp is the second part of a jump that occurs while coming down. The player does not have to jump; a stomp can be activated any time the playable tree friend is falling, whether from a ledge or a cliff. If the character stomps on top of an enemy or switch, he/she can defeat the enemy or activate the switch. Stomping on enemies is the tree friends' secondary attack in HTF Origins, HTFA Land and HTFA Maker, but it won't work on spiked or fire enemies (if attempted, the tree friend will take damage).
Anyone who can jump has the ability to stomp.