degree of freedom
A degree of freedom is one independent way a robot can move. Count up all the separate motions it can make on its own, and that number is its degrees of freedom — often shortened to DOF. A door on a hinge has just one: it can only swing open or shut. Your own arm has many more, which is why your hand can reach so many points in space and tilt at so many angles.
Each joint that bends or each slider that extends usually adds one degree of freedom. A robot needs enough of them to do its job: to place an object anywhere in front of it and also aim it in any direction, an arm generally needs six — three to choose the spot in space (left-right, up-down, in-out) and three to choose the orientation (the tilt and twist of the 'hand'). Too few, and there will be poses it simply cannot reach.
Counting degrees of freedom is one of the first things engineers do when sizing up a robot, because it sets the limits of what the machine can physically achieve. More degrees of freedom mean more flexibility and dexterity — but also more motors, more cost, and more complexity to control, so designers give a robot just as many as the task truly needs.
Hold a coffee cup and try to keep it level while moving it to every corner of your desk: you slide it forward-back, left-right, and up-down, and you twist your wrist three ways to keep it upright — that is six degrees of freedom in action, the same six a typical robot arm is built to have.
Three motions to choose where, three to choose which way it faces — together, full freedom to place an object.
Six degrees of freedom is the magic number that lets an arm reach any position and any orientation in the space it can touch.