How does a capacitor correct a power factor?

There are three possibilities

1. if initial power factor is in lagging and you introduced a capacitor in circuit. and the inductive reactance is more than capacitive reactance then only power factor increases.
2. If initial power factor is lagging and you introduced a capacitor in circuit. And now inductive reactance is less than capacitive reactance then there is a possibility of power factor enters into leading or it will be exactly 1(i.e. unity power factor).
3. If initial power factor is leading and you introduced a capacitor then power factor is decreases as leading power factor.
   

In the AC system, the power factor plays a very important role in the efficiency, voltage regulation, etc.

Ideally the power factor of the system must be equal to one(1).

This power factor can only be achieved by having purely resistive load.

Now in our day to day life, our usual electricity consumption comprises of inductors on very large basis in the motors(windings) and at many other different places.

Inductor has the power factor on a lagging scale. Hence, to balance that lagging p.f. to unity power factor (that of virtual resistive load) we need to have capacitors(which have leading p.f.)

Thus capacitors/capacitor bank help improve the power factor to level of 0.998 (~UPF).