The right to operate a flight between two airports, under the terms of the bilateral agreement between the countries. For US-China specifically, see https://en.wikipedia.org/wiki/Air_ro...ates_and_China

While open skies markets exist where carriers may launch any flights they want, they're not everywhere, and largely a recent development. PMCO couldn't even fly to LHR until just before the merger due to the lack of a route authority.