Sissy bar
A sissy bar, also called a "sister bar" or "passenger backrest" is an addition to the rear of a bicycle or motorcycle that allows the rider or passenger to recline against it while riding. Alternatively it can serve as an anchor point or support for mounting luggage or equipment that is not part of the bike.
Sissy bars for cruiser-style motorcycles are usually affixed to the rear fender struts, and are typically made of chrome-plated steel with a foam padded seatback for comfort. Some elaborate custom examples can extend three feet or more and often serve as mounts for novelty flags. A backrest for a touring motorcycle is often shorter and less elaborate and may be built into a top box.
On bicycles
Inspired by its motorcycle counterpart, a smaller version of the sissy bar was a common feature on 1960s- and 70s-era wheelie bikes, such as the Schwinn Sting-Ray and the Raleigh Chopper. This extended backrest, which attached to the rear of the bike's banana seat, gave a passenger something to lean back on and hold on to besides the rider doing the pedaling.
References
Dalzell, Tom; Victor, Terry (2015). The New Partridge Dictionary of Slang and Unconventional English. Routledge. ISBN 9781317372523.