The water analogy is most useful at this level (despite being wrong in most respects, it instils a basic working understanding good enough for the householder).
Think of a waterfall. Wait, think of two: a very high one with just a thin stream of water, and a low one, maybe a foot high with a torrent of water flowing over it (a weir).
Voltage is the height of the waterfall: a stream of water at the bottom of a very high waterfall will feel more painful than a stream from a much lower one.*
Current is analogous to the amount of water flowing over the waterfall - the river's current.
Multiplying voltage by current, you get power: the ability of the waterfall to do useful work.
(A very high waterfall with hardly any water flowing over it won't be able to turn a water wheel very quickly, and nor will a very low waterfall with a lot of water flowing over it. You need both voltage and current to do useful work.)
Re the movement of electrons: in fact they move very slowly on average under the influence of an electric field, but by their "bouncing against" their neighbours, the electric impulse is transmitted quickly through the conductor.
* An alternative analogue for voltage is water pressure, and indeed in some languages voltage is referred to as pressure.