Tom, an actual electrician I gather, came closest to answering the original question: Why does more volts require fewer amps? I'll add my 2-cents worth.
Water flow/pressure is a common analogy used to explain electricity for folks who are are uncomfortable thinking about electrons and dealing with units of energy, etc.: Amps would be like the amount of water going over a water fall, while volts is like the height (or pressure) of the water fall. The amount of work the water fall can do for you depends on the combination: the more height you have, the less flow you need, and vice-versa.
In reality, amps is a measure of how much charge (such as electrons in wires) moves past a point in a second, and volts is the difference in energy per charge that the electrons have after traveling between two locations (such as battery terminals). The units of charge and energy involve funny words like coulombs and ergs, and there's no need to go into them here.
The point is, just as the amount of gravitational work you can get out of a waterfall depends on both the height and flow of the water fall, the amount of electrical work you can get out of a battery depends on both the voltage and amperage of the battery. And, thus, for example, the wiring in a 12V system doesn't have to be as heavy as in a 6v because only half as many electrons are going to have to make the journey from one terminal to the other to release the same amount of energy and do the same amount of work.
By the way, you might have noticed the key word, DIFFERENCE, in the definition of voltage: There is no such thing as the absolute voltage at some point; it always must be measured relative to the energy the electrons would have at some other point.
