Capacitance is basically the capacity of a system to store charge in the system.
In a parallel plate capacitor, when we connect two plates of the capacitor with a battery using wires, the plates get charged by the flowing current.
Thats when we say that the capacitor is charged. If we remove the supply the capacitor cischarges and can give a supply of current to any device connected for some time.
If we insert a slab of dielectric material in the capacitor, the amount of charge stored can be increased as now the charge stored creates a field between the parallel plates, which now polarizes the dielectric material.
Thus more charge can be accumulated in it.