Our automatic watches are powered by a mechanical movement via spring tension. Inside, a rotor (called the balance wheel) moves with each movement of the arm, tensioning the spring. The spring then transmits the force to the hands via the mechanism. So the automatic runs completely without a battery - you can wind the spring both by moving it on your arm, and by manually winding the crown.
If you don't wear an automatic watch for a while, it will stop until you wind it up again via the crown and start it up again.