The Automatic Turret in Doom 3 is a base defense weapon located in the Mars research facility. 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 "battle" with one is in the Monorail Area, just before entering Delta Level 1.
The turrets cannot be destroyed by any means, but can be deactivated by finding a nearby control console and deactivating them. It is advisable, however, to let the turrets kill the demons in the area first.