As the damping force increases, the amplitude of oscillation of an object decreases at a greater rate. When the resistive force reaches a critical value, the object returns to zero displacement without being displaced to the other side.
This is known as critical damping. Of all the types of damping, critical damping makes the object reach a state of rest in the shortest time.
A car suspension system: after going over a road bump, the car suspension system quickly damps the oscillations of the springs supporting the tires, returning them to their equilibrium positions.
This reduces the discomfort of the passengers sitting in the car (from excessive oscillation/movement).