A camera's shutter determines how and when light gets recorded during an exposure. With film, the shutter is simply a spinning disc between the rear of a lens and the film strip. It has an opening that lets in light once per revolution for each exposure. When the light is obstructed, the film advances to the next frame and the process repeats. For these reasons, this type of shutter is often referred to as a mechanical or rotary shutter.
With most digital cameras, the shutter is controlled by the sensor itself. Photosites are read row by row in rapid succession, then reset between exposures, then read again for the next exposure. This simplifies things by reducing the number of moving parts, and permits full shutter angle control since film no longer has to advance between frames.
To learn more about global, rolling, and hybrid shutters, visit RED 101: Global & Rolling Shutters.