The intermittent movement of the projector is often called the crossbox. The reason for this becomes clear when you look at the animated picture on this page. The Maltese cross is the means by which a continuous drive is converted to an intermittent (stop and start) movement.
So why do we have to do this? Well, the human eye is tricked into seeing a moving picture by the simple illusion of showing a series of still images very fast. You may have seen flick books when you were a child - flicking the pages over rapidly made the characters move in a brief animation. A piece of film is also a series of still images, and in order to make us see a smoothly moving picture, it has to be projected at 24 frames per second.
At the far end of the shaft is the intermittent sprocket, whose teeth engage with the perforations on the film. The movement you can see at the near end is actually enclosed and running in oil inside the projector. The round wheel (known as the cam) is driven by the internal gears of the projector. As the striking pin on the cam rotates, it engages with one of the four slots on the Maltese cross, pulling it around by one quarter of a turn. This advances the sprocket, which in turn pulls the film through the projector gate. As the cam continues to rotate, it meshes with the curved face of the cross, which holds the film frame steady while it is being projected.
As you can probably guess, light must only be allowed to shine through the frame while it is stationary. A rotating shutter blade cuts off the light source while the frame is being advanced. If this shutter goes out of phase with the intermittent movement a flickering blur will be seen on screen. This is known as 'ghosting' and is the result of the frame being moved while being illuminated.