Car spark plugs run at ~12.000 V !! it hurts but a spark won't kill you. Wall outlet is 110V (usa?) but in CAN kill you.
This is a crude simplification but it might work:
Let's think energy as water. Your needs are expressed in gallons per minute, Amount of water that flows over a time span. You can have a really BIG pipe that water flows slowly and unrestricted, or you could have a tiny hose with lot of pressure that squirts a stream up to 3m ! ... the thing is, that it might be the case that if you have to fill a bucket, both scenarios may require the same amount of time. What matters is "amount of water moved in a certain time range"... And you cannot tell which scenario moves more water by watching the pipe size alone (or the water speed/pressure alone either)
...
So, the size or section of the pipe is current (Amps). The pressure/Speed of the flow is voltage. The flow (what matters!) is Power (Watts!)
The benefit, as was already told, is that by rising pressure (voltage) you may save money on smaller (cheaper) pipes (wiring, losses) while delivering the same flow (Watts!).
Hope it helps!