Ok i hope you know how a capcitors looks and its construction , this much basic is enough, so it got two parallel plates and some diaelectric between them ,now when its connected across a battery then the battery will add some electrons on one of the plates (let's say on the upper plate) but total electrons entangled in your circuit is always constant a power source cannot create or destroy electrons it just helps the electrons to move around in the circuit and create a potential diffrence, only that !!
So for every electron you add on the top of the plate (upper plate) you gotta remove the same amount of electron from the bottom of the plate
which means nothing but the charge accumulated (negetive charge) on the top of the plate is equals to the charge removed from the (postive charge) bottom of the plate, and they must be equal for the conservation of charge
This explains the phenomena nicely
