Degrees of Freedom
Refers to the freedom of motion of a system or joint. It is usually described as a subset from the allowed motions of a freebody in space, being it 3 independent translations and 3 independent rotations. When dealing with a system in the plane we consider only 3 allowed motions, 2 independent translations and 1 rotation.
When talking about a joint, it may allow a relative motion between the two or more conected links. The allowed relative motions are the degrees of freedom of the joint.