This is the involuntary shaking of one or both legs whilst climbing. Often caused by a surge of adrenalin and therefore usually at the most inappropriate moment (whilst delicately balancing on a very thin edge for example. This is usually quite funny to watch when it’s happening to someone else, but as is often the case is horrible when it’s happening to yourself.
It is called Elvis leg because of the obvious connection with “The King’s” trademark dance style. It is also known as “sewing machine leg”, especially when the shakes are fast and rhythmical or “disco leg” for the same reason.