[DonRotolo]

One story I've found to help people understand is a car's Cruise Control. We all know that it's a system used to keep a car moving at a constant speed.

P is the difference between the set speed and the actual speed. When P is non-zero, the system takes action to move this 'error' towards zero.

D is how fast you want to accelerate (or decelerate) back to the set speed. You may want to adjust this depending on engine power: with a very weak engine would want to go to full throttle quickly, with a very powerful engine you'd want to add throttle slowly. If you add too much power, you'd go past the set speed and have to slow down...the system would go too fast then too slow, continuously.

I is a little tricky, but basically it's fine control right around the set speed, allowing small speed errors to accumulate over time and allow for corrective action (like P) that is gentle instead of a large response (like D)