an aging aircraft is any aircraft that has been around long enough to "age", say a 1955 Cessna 150, for a random example. But I think this is a very general term, so I may be wrong.
Correct. The FAA began a program of special inspections and maintenance for a fleet of aircraft or an aircraft type that have reached a certain age. The FAA has issued Airwothiness Directives(AD's) that require special maintenance on these older aircraft.
Link to FAA: http://www.faa.gov/aircraft/air_cert/design_approvals/transport/Aging_Aircraft/