Definition
A set of one or more aviation red or aviation white lights, certified to FAA standards, that flash or rotate to make an aircraft conspicuous to other aircraft. Under 14 CFR 91.205, an approved anti-collision light system is required equipment for powered civil aircraft, and per 14 CFR 91.209 it must be operated during all flight operations unless the pilot in command determines that turning it off is in the interest of safety.
Plain English
A flashing or rotating light system on the airplane, built to FAA standards, that helps other pilots see you. The rules require the airplane to have one, and you must keep it on whenever you're flying unless leaving it on would actually create a safety problem.
Context Anchor
Seen in preflight checks, night flying rules, and discussions of required airplane lighting.
Derivation
"Anti-collision" simply means "against collision" -- the lights exist to help prevent mid-air or ground collisions by making the airplane easier to spot. "Approved" is the key word: it signals that the system is not just any flashing light, but one that meets specific FAA certification standards.
Why Pilots Care
The system is legally required for most night flights and many daytime operations; failure to have a working approved system can ground the aircraft and increases collision risk.
Intuition Check
Do not read “approved” as simply “a good light” or “a bright light.” Here it means the system is officially acceptable for that aircraft and its installation. Do not assume anti-collision lights prevent collisions by themselves. They only help others see the aircraft sooner.
Example Sentence 1
Before takeoff, the pilot turned on the approved anti-collision light system as part of the before-takeoff checklist.
Example Sentence 2
During the preflight inspection the student confirmed both wingtip strobes and the tail beacon met the requirements of an approved anti-collision light system.