This is the level of random variation in the pixels of digital photos. The pixels (photosites) on sensors record the levels of light falling on them as an electrical signal. However, there’s always a certain level of random background electrical activity which causes extra variations. A high signal to noise ratio means low noise levels, while a low signal to noise ratio means high noise levels.
The signal to noise ratio is affected by the size of the camera's photosites and the ISO (sensitivity) setting. Compact cameras have small sensors and hence small photosites, so their images are noisier right from the start, and this only gets worse if the ISO is increased. Maker use internal noise reduction systems to disguise the noise, and this can have a softening effect on the image.
Digital SLRs and hybrid cameras with larger sensors have larger photosites, so they don't produce anywhere near as much noise. As a result, their images look cleaner and clearer, and the picture quality is much better at high ISOs.