To hunt is to track and kill an animal for fun or food. In Italy, they use pigs to hunt truffles. In the US, they use shotguns to hunt deer.
Some humans hunt animals with a gun or a bow and arrow, and some animals hunt smaller animals — the way a wolf hunts rabbits or a cat hunts birds. You can hunt in a non-lethal way as well, like when you hunt all over your house for your lost car keys, or your little brother hunts for you during a game of hide-and-seek. The Old English root of hunt is huntian, "chase game."