There are two basic types of inverter available, known as modified sine-wave inverter and pure sine wave inverter, the former being the most common and least costly. Some appliances have been reported to not run on a modified sine-wave inverter, although the author has not experienced this with various inverters I've installed in RVs and boats.
The main function of an inverter is to convert direct current (DC) into alternating current (AC), and to change the voltage level into a stable 120 or 240 VAC that can be used by household appliances or "sold back" to the utility grid. The word "inverter" was originally used because the output wave form produced by its circuits alternates between a positive and a negative voltage. This device "inverts" the polarity of the power source (typically, a battery or PV array), causing the current to flow in alternating directions through the load. Hence the term "alternating current".