The elbow is dislocated when the joint surfaces of an elbow are separated. They can be either complete or partial. If complete, the joint surfaces are completely separated. If partial, the joint surfaces are only partly separated. This is known as a subluxation.
Dislocations of the elbow are not common, and typically occur when a person falls onto an outstretched hand. When one's hand hits the ground, the force from the impact is sent into the elbow. Typically, there is a turning motion during this force, which can drive and rotate the elbow out of it's socket. Elbow dislocations can also happen in car accidents when the passenger reaches forward to cushion the impact.
A complete elbow dislocation is extremely painful and is very obvious. The arm would look deformed and it may possibly have an off twist at the elbow.