Any tool in a game world over which a player exercises direct control is a doll. Sometimes the doll is represented by a human figure (often called an avatar), sometimes it is a ship, a car, pieces on a board game, a tetromino, a hand of God or a dot.
Some dolls are embodied, which means that the player uses them continuously and is "in" the world for the entire game. Others are disembodied, meaning that the player interacts with them intermittently and has no continuous presence of his own. Instead he floats above or drifts between different dolls as required.
Dolls are often extensible. As the player progresses through the game the doll might acquire new abilities that add further dimensions to the gameplay. In some cases these extensions are permanent, in others temporary. Dolls (particularly avatars) are also commonly customisable and considered a key way for players to self-express within a game.
In some games the line between doll and character can be blurred. A soldier in a Total War game behaves as a doll except for when his morale drops too low. Then he starts to run away and is out of the player's control.
The relationship between the player and the doll is not one of playing a hero in a story. Instead, it is the player projecting him or herself into the game world, similar to driving a car or manipulating a remote control toy. The player immerses himself through the conduit of dolls, but this means that the best dolls are usually the ones that have little definable personality of their own. The doll is not a 'player character'.