When a large amount of charge is stored on the plates of a capacitor, the strength of the electric field increases between the fields. If a dielectric is introduced between the plates, then it reduces the field strength between the plates and also reduces the potential of the plate. To bring the potential back to the initial value, more amount of charge can be stored on the plate. More the dielectric constant less is the electric field inside the dielectric. So, the ability to store charge increases. Also, dielectric should have large dielectric strength to avoid its breakdown when the large charge is stored.