If there was a contest to determine the King of Submission Holds, the armbar would be running at the front of the pack with the Rear Naked Choke. There are numerous versions of the armbar, from the Waki-Gatame (armpit armlock), Ude-Gatame (straight armlock), to Hiza Gatame (knee armlock), but I was to address the Juji-Gatame (Cross-Armlock).
This is the basic armbar that is a staple submission hold in MMA and many grappling arts, so much so that when one usually refers to a win via "armbar" that they are usually mentioning a submission coming from the Juji-Gatame. The greatest strength of the Juji-Gatame is that it is extremely versatile and can be applied from a great variety of positions: the guard, the mount, sidemount, the back, standing or even from "flying" positions.
The armbar works by securing the movement of your opponent with your legs. One leg isolates the movement of the opponent's body away from the extended limb, while the other isolates the movement of the opponent's head. Once the opponent's arm is in position, and their elbow is secured across your hip or leg, the submission pressure is created by arching the hips up against the range of movement of the elbow. This can result in muscle, tendon and ligament damage, even dislocation, or bone fractures.
Instruction on how to apply the Juji-Gatame from the top by Gokor Chivichyan here
Instruction on how to apply the Juji-Gatame from the bottom by Cesar Gracie here
Rumina Sato's infamous flying armbar on Charles Taylor here
The helicopter armbar can be seen here