Autofire is a device built into a joystick which keeps triggering the controller's fire button at a steady rate. This trigger finger saving feature is most common in the digital Atari-style joysticks supported by the majority of computers and game consoles in the 1980s and early 1990s. QuickShot models were probably among the first sticks to be equipped with an autofire option.
Autofire is usually implemented using a simple oscillator (like an LM555 plus a few analog components) which generates pulses to the fire button button circuit (pins 6 Button1 and 8 GND on an Atari-stick) at fixed intervals. The circuit is usually powered from the +5V pin of the joystick port. All autofire-equipped joysticks have a switch to toggle the autofire mode on and off. More advanced models also contain things like firing rate adjustment dials and autofire-when-button-depressed modes.