A hand-held chalkboard with a hinged arm attached to the stop. Used when making films. At the start of a take, the clapper is held in front of the camera with the take number written on it (for reference when editing the film) and the arm is snapped shut.
When a film is being recorded, the sound and the pictures are (or were, back in the day) recorded on separate equipment.
Later on, when the film is being edited, it is necessary to get the sound recordings and the picture recordings in perfect synchronisation.
The point of the clapper (or clapperboard) is to make it easy to do this - you just have to find the part of the audio track where you can hear the clapper is banged, and line that up with the part of the film where you can see the clapper slamming shut.
Nowadays, naturally, this is achieved using some technology that would require an electronics degree to understand.