A type of Gun that uses a lever to cycle the action. After a round is fired, a lever around the grip is pushed and then pulled back to eject the casing and chamber a new round.
Commonly used in the American Frontier era, it is therefore a normal fixture in cowboy or Old West-themed fiction. Arnold Schwarznegger's lever-action shotgun in Terminator 2 is a recent usage in a modern setting.
Basically, if a Rifle or Shotgun has what looks like a handguard around where the character holds the gun (grip), it is very likely a lever-action gun.