here's how I understand it:
the units that Watts represent, is Work/second. (work is the force exerted over a distance, which is Joules).
that means that in theory if you had an electric car, and accelerated fast enough to hit 60mph in 5 seconds, the amount of electricity used would be equal to if you hit 60 mph after 10 seconds. however the watts would be considerably higher.
I think of voltage as the energy within the electric flow (though that is somewhat misleading I think). the unit for Voltage is J/C or Joules/Coulomb. a Coulomb is a certain amount of electrons. 1 electron is (I think) 1.6X10^-19 Coulombs.
in order to convert from Volts to watts, you need at least one other number. the main equation for this is Watts=Amps*Volts.
Amps is basically the amount of coulombs passing a given point in a second.
so you end up with Coulombs/second * Joules/Coulomb= Joules/second.
the hardest part for me to understand is the Voltage one.. it's kind of a weird idea. it's the amount of work you can do with a charge that is in an electric field (I think).
you think that's hard? try understanding magnetism. it's SOMEWHAT like electric fields, but different. I don't like the explanation of what it is in todays science.. it doesn't make sense to me.