Autopilot is a system that controls the course of an airplane or ship. If the captain of a ship is using autopilot, she can take a break from manning the controls herself.
When a plane is on autopilot, it's not exactly flying itself, but it's set to maintain a course or altitude while the pilot concentrates on other details of operating the airplane. Autopilot is short for automatic pilot, and the first such system for aircraft was invented in 1912. The nickname came later, in the 1930s. The slang meaning of autopilot is "out of habit," as when a sleep deprived worker goes through his whole day on autopilot.