Camera Shake is a fault in a photograph caused by the camera not being held still enough while the exposure was made. The result is a blurred, or sometimes a double image. Camera shake is more probable in low light or using slow film, where slow shutter speeds are necessary, and when using long (telephoto) lenses which exagerate movement.
Camera shake can be reduced by using a support - e.g. a tripod, holding the camera braced against something solid (such as the photographer!), or using a higher shutter speed, faster film or shorter lens.
Some cameras designs can increase camera shake. Layouts such as the "chocolate bar" format common on 110 film cameras (e.g. the Haking 220 EF or Kodak Pocket Instamatic 60) are awkward to hold steady; a light weight camera can also make camera shake more likely. SLRs - particularly lightweight ones like the Pentax MV - with large, fast mirror movements can suffer from shake; this form of shake is called mirror slap.
Of course, sometimes camera shake is done deliberately, for effect.
Many digital cameras feature shake reduction systems (also known as vibration reduction (VR), and other names), which can be implemented by physically moving the lens or image sensor (perhaps using piezo-crystal driven actuators), or by removing the movements electronically, in software.