In the broadest sense, and in the context of this forum, hunting is finding some critter to shoot, and killing it.
There are many parts and pieces to the whole deal, of course. You can scout around to find the biggest buck in the pasture, which means a good bit of looking without shooting. Ya gotta find most all of them before you can know which is the biggest, right? Then ya gotta find that big SOB a second time--and that's not necessarily the easiest deal going.
But, it means you've spent a good bit of time outdoors, "just lookin'".
You can hunt for pestiferous critters, like ol' Wily Coyote.
If you sit, you're hunting in the same way as a cougar, in ambush. You can play sneaky-snake in thick-ish cover country or serious brush/jungle. Or you can just walk across country and work the wind. It's all some form of hunting, but in different styles. The style is forced by terrain, cover and one's level of skill or physical strength.
Purpose? You can hunt for meat, or trophy and meat, or for varmints. It's all a part of the package called "hunting".
Art