Played by multiple players, cooperatively or competitively, locally or remotely.
Multiplayer refers to a game that can be played by several players simultaneously. Opposite of single-player, though many multiplayer games do include a single-player mode.
They may be playing together in the same physical location (known as local multiplayer, e.g. Tennis for Two) or over a network (known as network multiplayer; requiring networking). Some genres, such as mmorpgs, are always network-multiplayer by definition.
Local multiplayer can be implemented as simultaneous (by giving each player a separate controller or other input scheme, sometimes different control schemes entirely), or as hotseat multiplayer in which players take turns using the same physical controls (Worms: Armageddon is a famous example).