A backup system was a means of restoring lost computer data or functionality, including the operations on a starship or space station.
In 2268, after intentionally crossing the Romulan Neutral Zone and entering Romulan space, thus violating treaties, Captain James T. Kirk of the USS Enterprise lied to a female commander that it was due to instrument failure which caused navigational error. The Romulan commander was skeptical that such radical instrument failure on one of Starfleet's finest vessels would go unnoticed until they were well past the Neutral Zone. The malfunction of backup systems was a reason given by Kirk in response. (TOS: "The Enterprise Incident")