What is the function of Capacitor in AC and DC Circuit?

A capacitor is two conductors separated by an insulator. If you apply a DC voltage the capacitor will charge and then it will store that charge for a while. So it acts as a filter, absorbing charge when voltage rises and releasing it when voltage drops.

In an ac circuit the capacitor is constantly charging up or down toward the changing voltage. That means the current and voltage are time related functions of each other.

Functions might be called a lot of names: filter, bypass, swamp, coupling, and others.