One of Tesla's legacies (and that of his business partner George Westinghouse, boss of the Westinghouse Electrical Company) is that most of the appliances we have in our homes are specifically designed to run from AC power. Appliances that need DC but have to take power from AC outlets need an extra piece of equipment called a rectifier, typically built from electronic components called diodes, to convert from AC to DC.
An inverter does the opposite job and it's quite easy to understand the essence of how it works. Suppose you have a battery in a flashlight and the switch is closed so DC flows around the circuit, always in the same direction, like a race car around a track. Now what if you take the battery out and turn it around. Assuming it fits the other way, it'll almost certainly still power the flashlight and you won't notice any difference in the light you get—but the electric current will actually be flowing the opposite way. Suppose you had lightning-fast hands and were deft enough to keep reversing the battery 50–60 times a second. You'd then be a kind of mechanical inverter, turning the battery's DC power into AC at a frequency of 50–60 hertz.
Photo: A typical electricity inverter. This one is made by Xantrex/Trace Engineering. Photo by Warren Gretz courtesy of US Department of Energy/NREL (DoE/NREL).
Of course the kind of inverters you buy in electrical stores don't work quite this way, though some are indeed mechanical: they use electromagnetic switches that flick on and off at high speed to reverse the current direction. Inverters like this often produce what's known as a square-wave output: the current is either flowing one way or the opposite way or it's instantly swapping over between the two states: