The degrees of freedom (DOF) of a mechanical system are the number of independent parameters that completely describe its position or configuration. A rigid body in three-dimensional space has at most six degrees of freedom: three translational (movement along the x, y and z axes) and three rotational (rotation about those axes, i.e. roll, pitch and yaw).
In robotics, each degree of freedom typically corresponds to an independently actuated joint that provides linear (prismatic joint) or rotational (revolute joint) motion. The number of degrees of freedom determines how flexibly a robotic arm can set the position and orientation of its end effector.
An industrial robot arm usually has six degrees of freedom in order to reach any position and orientation in space. Robots with more degrees of freedom than the task requires are called redundant and can avoid obstacles or choose multiple paths to the same goal.