What is an automatic handgun?

It depends on what you mean.

1. If you mean semi-automatic (sometimes referred to as automatic), it means a handgun that auto-loads the next cartridge in order to fire it, but fires only one cartridge for each pull of the trigger.

2. If you mean a full auto, it means a handgun that will continue to fire as long as you hold the trigger, or until it runs out of ammo.