ArduPilot supports several kinds of object avoidance. Avoidance of Airborne Vehicles (ADSB) and Object Avoidance (Object/Ground/Ceiling).
Supported types vary with vehicle (Plane only supports ADSB). Some kinds of avoidance require external hardware, such as ADSB receivers or Rangefinders.
Various strategies are employed and vary depending on vehicle, mode, and/or object to be avoided. Re-routing, slide, stop, or failsafe style actions are the most common ones. See the particular Avoidance Feature below for details.