An airbridge is another name for a jetway, a corridor from an airport terminal to an aircraft for secure boarding.
You can use an airbridge in Microsoft Flight Simulator X by pressing Ctrl + J.
A jet bridge (also termed jetway, loading bridge, aerobridge/airbridge, air jetty, portal, passenger walkway or passenger boarding bridge) is an enclosed, allowing passengers to board and disembark without having to go outside.
The building that contains the aircraft gates is the terminal building of the airport. The usual name for the halls on which the gates are located is a concourse. The name for the retractable walkway that connects to passenger airplanes for boarding is a "jetbridge" or "airbridge" or the trademark term "Jetway" which is sometimes used generically.