Character invasions are a form of multiplayer where a playable character can invade another player's world. Invasions can be forced, or initiated by the player. The invader does not have to be a playable character. Some invasions may be plot related, by recurring invaders, or by otherwise friendly NPCs.
The Souls series red invaders do not draw aggro from or cannot be damaged by enemies. Purple invaders, introduced in Dark Souls 3, can be damaged by enemies and the host.
Gray phantoms in Dark Souls 2 are forcefully drawn into another player's world, and must either kill the host, or escape through a fog wall.