A spirit, usually a demon, a ghost, an angel or another supernatural being takes control over someone's body and uses it as their own, forcing the host to act like the spirit wants. They may use it either as a spying tactic, or to be immortal (often by possessing a body and passing into other when the first gets old), or to use the host's powers (if has). Anyway, the spirit usually will do this in order to promote their own agenda.
What happens with the host's mind/soul may vary. They may be unconscious and not remember nothing when the spirit gets out, or they could be conscious and be a spectator from their own body, but being unable to do anything for their own will. Or the former owner's soul is now out of the body. Regardless, the possession may be visible by Mind Control Eyes or not.
Sometimes, the possessed character will get free after Fighting From the Inside, via Heroic Willpower or Hollywood Exorcism. Yet, some characters can't be possessed. It may be because they're too crazy, have a Psychic Block Defense, use magic, or because A Wizard Did It. Then, spirits that might possess people won't be able to invoke this trope on these people.
Compare Mind Control Device, Hypnotic Eyes and Mind Control Eyes (that do this from outside), Grand Theft Me (when who does this is a human), Puppeteer Parasite and The Virus (when what does it is a parasite, often an alien), and People Puppets (when the person moves are controled by a Living Doll Collector but the "puppet" usually knows what happens).