A missile weapon is a weapon which throws missiles. This means that, generally, it does no harm in and of itself (being in simpliciter a delivery mechanism) but projects, in some way, a missile so as to do harm at a distance.
In general they come in three varieties, all of which employ methods to store energy, so that it can be accumulated and then released.
One method is the "bow", where the weapon tends to be long and pointy, the energy is stored in the equivalent of a bow-string, and on release the missile flies and (all being well) hits and hurts the target.
A second stores the energy by twisting a cord or series of cords, which apply rotation to an artificial arm (much as muscles apply rotation to a cricket-bowler's arm) and project a generally roundish missile (a rock, bomb or dead and diseased cow) a distance.
The last requires alchemy to produce an explosive mixture, which is placed at one end of a tube. A ball or bullet is then introduced into the tube, and when the explosive is ignited, the ball is thrown out.