The three terms are proportional (react to the current error), integral (eliminate a small error that refuses to go away, such as gravity pulling a joint down) and derivative (damp the motion so it does not overshoot and oscillate).
Each term has a gain that has to be tuned. Too much proportional gain and the joint buzzes; too little integral and it never quite reaches the setpoint; too much derivative and it becomes noisy and sluggish.
PID runs in the current and velocity loops of practically every robot joint, in temperature control of a 3D printer hotend and in the altitude hold of a drone. It needs no model of the system, which is why it survives next to far more advanced control methods.
