The "unit" used for electricity (kWh) is actually a unit of "energy" whereas the Watt is the unit of power.

And Energy = Power* Time. (Watt*hours)

Every electrical equipment/appliance has a wattage that gives us a measure of the "Rate of electrical energy consumed by it",

i.e. how much energy does it continuously consume to do work in a given period of time.

Therefore, We Pay for the "energy" that we consume at our home. Our equipments consume this energy at different rates.