An FAA violation is in many ways exactly what it sounds like. Any time you violate any of the rules about flying your particular class of aircraft, you’re likely to encounter one of the classes of FAA violation.
In essence, the FAA governs the safe operation of aircraft, within a framework of national and where necessary international aviation law. This framework covers everything from safe runway operation, the training and certification needed to fly various classes of aircraft or to fly in various types of weather, to the correct procedure and limits of fueled flight. Rights of way, near-misses, navigation, and obedience to instruction from land-based flight control stations, all come under FAA jurisdiction.
That means all the things you learn as a pilot at various levels – from your Private Pilot’s License through to your Commercial Pilot’s License and your instrument rating – are subject to the rules of safe aviation, as defined and operated by the FAA.
Break any of the rules, intentionally or accidentally, and you violate the FAA’s rules. Given that your license and certification to fly particular classes of aircraft are granted by the FAA, the Authority can implement actions to correct, censure, revoke or suspend your license, or to impose financial fines, to ensure the safety of the skies and to encourage future compliance.
That is why there are several classes of FAA violations – and similarly, several classes of actions the Authority can take to deal with those infractions. The lightest type of actions, the Administrative action, might well be only the equivalent of a letter outlining what you did wrong - a written warning, essentially.
The FAA can make you re-sit your examinations, though, if it feels you need the refresher. It can suspend your license or your certificates, restricting you to particular types of flying. Or ultimately, it can revoke your license to fly at all, or move into either civil or even criminal actions if your actions had a strong likelihood of causing major harm to many people.