When you watch a movie in a theater, the screen is dark half the time. You can't tell it's dark because of the physical principle that makes a rapid sequence of still pictures appear to move: persistence of vision. The human eye can't distinguish between images that flash by 17 times per second or faster. Movie film runs through a projector at 24 frames per second. Each frame is held for a split second behind a rotating shutter while light is projected through it. The shutter opens and closes three times for every frame - cutting off the light and restoring it so quickly that the audience can't perceive it. The film advances when the shutter is closed, so you don't see the edges of the frames as they flash past.
Sources: howstuffworks.com; 'The Camera and the Film' (Time/Life Books); 'The Book of Movie Photography: The Complete Guide to Better Moviemaking' by David F. Chesire (Knopf, 1979).