Energy is defined (scientifically) as "the ability to do work", which admittedly does not in itself really make things clear. It's basically the oomph required to get something done: the amount of heat that must be added to a tea kettle to get the water inside from room temperature to boiling, or the exertion required to haul a weight up a hill, or whatever. A measure of energy does not tell anything about how fast the work happens, just what it takes to make it happen.
Power is the rate of energy transfer. More power means more energy is expended or used or whatever in a given period of time, and the work can be done more rapidly. A small, one horsepower engine could move an RV up a hill, very slowly; a 300 horsepower engine also can get it up the hill, but at a much more rapid rate. (It won't be 300 times as fast, but that's due to increased frictional losses from air resistance, etc. The amount of energy required to overcome gravity, ignoring other losses, is the same in either case.)
Watts are a measure of power, or rate of energy usage. The quoted blurb gets that reasonably correct, especially if you disregard the reference to amps (which, of course, are measuring electrical current flow--and in this particular case that is approximately an equivalent measurement, in practical terms, because the voltage remains more or less constant-ish.)