A power inverter is an electronic device that changes the DC or Direct Current (eg. 12V) to alternating current (AC, usually 120V or 220V). They are commonly found in RVs, on boats or in off-grid houses, wherever there is a need of powering popular AC devices with a DC current stored in batteries or delivered directly from renewable sources such as solar or wind.
If you want to run not just simple kitchen appliances, but more advanced microcomputer-controlled devices, you will need to spend a little bit more and invest in a pure sine inverter. Electricity they generate matches a higher standard and closely resembles the power produced by your public utility services.
Inverters range from very small that can be plugged in your car's cigarette lighter socket, to very big ones that can handle kiloWatts of power. The calculation is simple, just sum up the power requirements of all your AC (120/220V) devices intended to use at the same time. Your inverter has to be able to provide more than that.