The least number of mutually independent parameters (coordinates) required to uniquely define a material system’s position in space, time, etc.
A material point moving in three-dimensional space has three degrees of freedom. A rigid body in three-dimensional space has six degrees of freedom: three linear coordinates for defining the position of its center of mass–or any other its point–and another three Euler angles defining relative rotation around the body’s center of mass. A disk rolling without slipping over a horizontal base has one degree of freedom, corresponding to the position of its center along the base or rotation angle measured from the horizontal line. A disk rolling with slipping has two degrees of freedom.