Smotherbox (or smothering box) is a type of dungeon furniture similar to a queening stool. It may be used in face sitting, where the Dominant sits on the face of the submissive, for the purpose of receiving oral sex from him or her.
A smotherbox has two openings. One is in a vertical side of the box for the sub's neck (the head is of course inside the smotherbox); the other is on top of the box to expose the face. The inside of a smotherbox is often padded to provide support for the sub's neck, and to prevent their head from moving.