Among many other responsibilities, they inspect airports, flight schools, and charter operations; hold safety seminars; give flight tests; conduct ramp checks; and investigate accidents. They administer the FAA's Wings pilot proficiency and PACE (pilot and aircraft courtesy evaluation) programs. FSDOs also manage the systems for the registry of aircraft and all official airmen records.
As you progress in your training, you can look to your FSDO as an information resource (did you know some offices have free lending libraries of aviation safety videos?). Those who are ready to take a checkride can contact their FSDO to arrange for a free flight test. (Do not ask a designated pilot examiner to give you a free flight test; DPEs are not FAA employees - they provide examiner services for the FAA on a fee basis.) You can attend free Wings safety seminars and, if you hold at least a private pilot certificate, when you successfully complete one or more phases of the Wings program within a specified time period you get credit for a flight review. After you purchase an aircraft, the FSDO is where you'll obtain an airworthiness certificate. And, should you desire to take your love of aviation safety to new and lofty heights, the FSDO is where you can apply to become an Aviation Safety Counselor (if you are a CFI, ATP, or A) or an Aviation Safety Associate. These individuals volunteer their services to promote aviation safety at their local airports.
To find your FSDO, go to the FAA Web site, click on the region in which your state is located, and choose the office that's closest to you. If you want to visit, call in advance and make an appointment (drop-in visits ceased after September 11, 2001).