The proportional constant utilizes present data. This is number that is multiplied by the current error to achieve a motor speed. Using only a proportional control will result in something called steady state error where the robot will hover at a degree measure close to but not exactly the commanded turn angle. The proportional constant gets the robot close to the commanded angle.

The integral constant utilizes past data. This constant sums all past error values and then multiplies it by a very small number to achieve a motor speed. This constant prevents steady state error because if the robot has been stuck a few degrees off of the commanded angle for a long time this will kick in to give it that final push. The proportional constant acts as a final push to get the robot to a commanded angle.  

The derivate constant uses the predicted future data. This constant calculates the rate of change of the error and adds a damper if the rate of change is too high. This is usually a negative value, so it is inversely proportional to the instantaneous rate of change(derivative). The derivative constant can see if the robot is approaching the commanded angle too quickly and slow it down if it is about to overshoot.