The Automatic (or Automated) Turret in Doom 3 is a base defence weapon located in the UAC base on Mars. It was designed by the Mixom Corporation as a security system, and can be first seen when entering the Marine HQ. However, the demonic invasion of the facility caused the Identify Friend or Foe (IFF) program in the turrets to malfunction, resulting in the turrets targeting anything that moves.
Your first encounter with a live one is in the Monorail Area, just before entering Delta Labs Sector 1. Fortunately, if it is not deactivated immediately, the turret will helpfully kill several enemies.
The turrets cannot be destroyed by any means, but can be deactivated by finding a nearby control console and deactivating them.