Shotguns come in many shapes, sizes, and types. Popular actions include pump action (a.k.a. slide action), semi-automatic, single-shot, double barrel side-by-side, double barrel over/under, and even bolt action. Some lever action shotguns have been built, but not many.
The shotgun gets its name from the fact that it usually fires a shotshell, which contains shot. These metal pellets come in many different sizes, and can be used for a number of different purposes. Smaller shot is to be used on birds and whatnot, while the largest shot is meant for hunting big game such as whitetail deer.
The bore of a shotgun barrel is usually smooth, without rifling. Those shotgun barrels that do contain rifling are meant for shooting single projectiles known as shotgun slugs, and are, in effect, rifles with extra-large bores.
Shotguns are possibly even more popular than rifles. Hollywood has demonized and/or glorified the shotgun until many people are convinced that sliding the forearm on a pump shotgun will strike fear into intruders (mine will be loaded and ready long before I put myself at risk defending against prowlers), while others think that anything shot with a shotgun will explode (not true). These things have contributed to the fascination many people have with shotguns.
Shotguns are used by hunters of large and small game, home defenders, law enforcement, and military personnel. It is one of the oldest types of firearms in use today, and is still immensely popular.