The Freedoom project aims to create a complete free content first person shooter game. But Freedoom by itself is just the raw material for a game: it must be paired with a compatible game engine to be played. The download page lists some recommended ones.
id Software released the source code to their classic game, Doom, under the GNU General Public License. This means that the program code that powers Doom is free; Freedoom complements this with free levels, artwork, sound effects and music to make a completely free game.
Freedoom is actually three games in one, consisting of two single player campaigns and one set of levels intended for multiplayer deathmatch (FreeDM).