1) Any scheduled air service performed by aircraft for the public transport of passengers, mail or cargo.
2) a flight or a series of flights carrying passengers, cargo or mail for remuneration or hire.
1) ICAO, Official definition, DOC 7300 Convention on International Civil Aviation /8, 2000, p. 43, Art. 96
2) COMMISSION REGULATION (EU) No 255/2010 of 25 March 2010 laying down common rules on air traffic flow management
Air service, in its broadest sense, includes any service performed by aircraft for public transportation, whether on a scheduled or non-scheduled basis. For regulatory purposes, however, the term always has a specific meaning (defined in Article 96(a) of the Convention on International Civil Aviation and used in most bilateral air transport agreements between States) and refers to any scheduled air service performed by aircraft for the public transport of passengers, mail or cargo. (Note source: ICAO Terminology and Reference Database)