Capacitor has the dielectric material in between the plates and the plates are separated by a distance"d".
Due to above operation, we said current is lead as compared to the voltage in the capacitor.
When ever a potential difference is applied across the capacitor plates, the dielectric material of the capacitor plates has the dielectric material ions. These ions are firstly vibrating due to potential difference and then the positive ions of dielectric material are moves towards negative plate side and the negative ions of the dielectric material are moves towards the positive plate of the capacitor.Due to this movement of dielectric material ions, a small displacement current is produced in between the plates and then some voltage is appears across the capacitor plates.