Your question is not clear... You asked one thing in a subject and another in the question body....
If you are asking why flashing MULTIPLE times - the three answers above me are correct and do a decent job explaining what's going on.
If you're asking why flashing TWICE (and I mean exactly twice in very rapid succession) - there's a completely different reason, and cameras do it even when red eye reduction mode is off and even with the external flashes:
This is all due to camera's attempting to determine just how much light flash needs to emit in order to take a properly exposed picture. In technical terms it's called "flash metering". When you press the shutter button - a very quick flash is fired (we call it pre-flash), but no picture is taken, instead camera "looks" at what happened and how much of the light the flash emitted came back to the lens. Then, armed with that knowledge, the camera can figure out exactly for how long a main flash should be fired to expose the scene properly. At that time, the shutter is opened (on some P&S cameras metering through the matrix it will first close after metering and then opene again for exposure, on SLR's a mirror will flip then shutter will open), a flash will fire for calculated amount of time, then shutter will close. Done! Picture taken.
So, unfortunately, as annoying as the pre-flash may be - it is almost impossible to get rid of it. And I know for myself, that on some models of cameras the time between the pre-flash and main flash is such, that most sensitive and quick of us will have time to react and close or start closing their eyes, just to be with closed eyes in the shot!
There are really two ways to deal with the above situation. One is to actually shoot in fully manual mode. Not all cameras can do this. This means both camera shutter/aperture set manually AND flash output level set manually. But then you'd need your own flash meter to measure the exposure, or to experiment a lot! Second is to actually turn on the red eye reduction, so that the flash does a series of pre-flashes, like people above said, allowing those blinkers to do their blinking routine and be back with open eyes for the main flash and the resulting shot!
LEM.