What is a PID controller and what do P, I, and D represent?

A PID controller uses three terms: Proportional (P) provides output proportional to current error (faster response but steady-state error), Integral (I) sums past errors to eliminate steady-state error (adds lag), and Derivative (D) predicts future error from rate of change (improves stability and reduces overshoot). The controller output is: u(t) = Kp*e(t) + Ki*integral(e) + Kd*de/dt. PID is the most widely used industrial controller due to its simplicity and effectiveness.