When you turn the power switch to the on position, an electric circuit connects the negative and positive terminals of the batteries together.

This is a very simplified version of an electrical circuit.

 Electrons flow from the negative terminal, through the camera, to the positive terminal of the other battery.  The electrons continue to flow around this circuit, receiving energy from the batteries and delivering this energy to the camera until the camera is turned off or the batteries die (see How a battery works to change dead batteries).