Chapels in churches are often alcoves. Picture one set off to the side with a vaulted ceiling, separated by pillars and a small railing. See that and you see an alcove, defined.
If your bed is in an alcove in a studio apartment, it is in a recessed area of the room, separated by an arch or a half wall but not by a door. Think of an alcove as a sidecar to a room or even a cave. It's a separate smaller area that is still attached, but feels cozy because it is partially enclosed.