The Snickometer (known as 'snicko' for short) was invented by English Computer Scientist, Allan Plaskett, in the mid-1990s. Snickometer technology was first used in 1999 by Channel 4 in the UK, before being used in India and Australia.
The snickometer is composed of a very sensitive microphone located in one of the stumps, connected to an oscilloscope that measures sound waves. When the ball nicks the bat, the oscilliscope trace will pick up the sounds. At the same time, a high speed camera records the ball passing the bat. The oscilliscope trace is then shown alongside slow motion video of the ball passing the bat, and by the shape of the sound wave you can determine whether of not the noise picked up by the microphone coincides with the ball passing the bat, and whether the sound seems to come from the bat hitting the ball or from some other object.
This technology is used in televised cricket matches to graphically show the video of the ball passing the bat at the same time the audio of any sounds at the time. It is only used to give the television audience more information and to show if the ball did or did not actually hit the bat. The umpires does not get the benefit of seeing 'snicko'.
As the ball passes the bat, there can be other noises that can be confused with the ball on bat noises. The bat often hits the pads on the way through, making a sound at the same time the ball passes the bat. The sound/sound wave is purpotedly different for bat-pad and bat-ball, but this is not always clear. The shape of the recorded soundwave is the key - a short sharp sound is associated with bat on ball. The bat hitting the pads or the ground produces a flatter sound wave.
Note that the umpire does not have the benefit of the snickometer, and must instead rely on his senses of sight and hearing, as well as his own personal judgement.