This term is used and abused in most walks of control theory. The core thinking is that a controller makes a controlled value aka "actual value" follow a reference value aka setpoint.
The controller does so by amplifying the difference between actual value and setpoint. If actual value is too low, the controller increases its output to correct it. The gain that such a controller has is called a proportional gain. If the gain is, for instance, ten times - then the output is ten times the difference. The proportional gain gets a shorter name "P".
The fact that there has to be a remaining difference to keep controller output at the desired value is very often a problem. It makes the P controller steer the actual value close to, but not exctly to, the setpoint.
By introducing an integrating action that makes the controller output increase as long as there is any error at all, no matter how small, a PI (Proportional-Integrating) controller is created. The PI controller integrates the difference and adjusts its output to keep actual value exactly same as setpoint.
A PI controller is very often all you need. Most drive systems work very well with a PI controller for speed and a PI controller for torque. The output of the speed controller then is the setpoint for the torque controller.
But, there are situations where a PI controller simply doesn't react fast enough. It is then possible to antecipate deviations by taking the time derivative of the control difference. The controller will then be able to act forcefully to fast changes and this part of a controller is - of course - named Derivative action. So a combination of these three controller actions is a PID controller.
Gunnar Englund