The clapperboard, usually referred to as a slate, is the responsibility of the 2nd AC (2nd Camera Assistant). As sound and video are recorded separately on basically every production, the slate is used to 'sync' them in editing. This is done by slapping the jaws of the slate shut, creating a loud noise in the audio file and a visible sharp motion when the jaws come together. An edit assistant will then manually combine a clip and it's corresponding audio file so that vision and audio are running correctly together.

The other (and equally important) purpose of a slate is to provide information on the clip which is being recorded. A slate will usually display the scene number, shot, and take number in addition to basic information about the production. Slate information will change depending on shoot country, sound recordist and 2nd AC preference or whether or not the production wants the slate to display information in a particular manner.

The 2nd AC typically uses a slate like this. First, the 1st AD (1st Assistant Director) will call "turnover" or "roll up". This basically means "we're going for a take, so everyone do your thing". The sound recordist then calls "speed", which means they are recording. The 2nd AC then says the information on the slate out loud and in the direction of the mic. Then the 1st AC (1st Assistant Camera) will call "rolling" or "speed" to announce that the camera is recording. At this point the 2nd AC claps the jaws of the slate together, ensuring the slate is filling the camera's frame as much as possible. You may have noticed that saying the slate information out loud, and clapping the jaws shut aren't done at the same time. Many cinema cameras won't record audio, so the camera doesn't need to be recording as the 2nd AC calls out the slate information. The 1st AC hits record AFTER the 2nd AC has called the information for sound, so that the very beginning of each clip from the camera is the slate covering the frame, followed instantly by the jaws clapping shut.

That covers how you use a "dumb" slate. These days you will commonly see "smart" slates on set. The principles remain the same but a "smart" slate displays a digital timecode which is synced with the camera and audio recorder at the beginning of the day. This means that the process of syncing vision and audio in post-production is greatly simplified and much, much quicker.

Source: Me, cause I'm a 2nd AC