What DOF actually means
Degrees of freedom, or DOF, count the independent ways a robot can move, usually corresponding to the number of controllable joints. A simple 2-joint arm has 2 DOF and can only reach positions within a flat plane in front of it. A typical industrial arm has 6 DOF, enough to place its end effector at any position and orientation in 3D space, the minimum generally needed for full, unrestricted spatial reach and rotation.
Humanoid robot arms, and human arms themselves, often exceed 6 DOF. That extra flexibility is called redundancy, and it means the arm can reach the same target position and orientation through multiple different joint configurations, similar to how you can touch a doorknob with your elbow in several different positions while your hand stays put.