[DonRotolo]

Cruise control in a car is one example of PID. As you approach the setpoint (the speed you want), the car accelerates less and less until it is at the right speed, as opposed to accelerating at maximum until it hits the speed and then lets off the gas suddenly. Then it keeps that speed, even if there's a hill. The further below the set speed you are, the greater the acceleration - to a point: There is a maximum acceleration value that the car won't exceed (maybe about 40% of the car's maximum performance).

P is the gradual lessening of acceleration as the "error" (the difference between the set speed and the actual speed)

I is what keeps the speed constant, even when the error is very small

D is what limits the maximum acceleration to a safe and reasonable value.

In robotics, often P is all you need. Maybe I, rarely D.

Here on CD, look for a paper called "PID without a PhD", as well as the several dozen posts on the topic.