As an analogy, if you have a hose squirting out water at a certain rate, and you increase the pressure, then all other things being equal you'll get a higher rate of water. But then that means you could now reduce the size of the hose, keeping the new higher pressure, and achieve the original rate of water delivery with a smaller, cheaper, lighter hose.

It's very similar with electricy: water pressure is voltage and the rate of water delivery is power.