What is the purpose of integral action in a PID controller?

Integral action eliminates steady-state error (offset) that exists with proportional-only control. It continuously sums the error over time and adjusts output until error becomes zero. The integral term (Ki * integral of error) increases as long as any error exists, eventually driving the process variable to exactly match the setpoint. Integral time (Ti) or reset rate determines how fast this correction occurs. Too much integral can cause overshoot and oscillation.