Inverters are used to convert the direct-current (DC) electricity from a battery into alternating-current (AC) electricity that can then be used to power household devices.
Choose the wattage of your inverter based on the maximum wattage of your load. Make sure to consider surge currents if you are using devices that have high start-up currents, like motors or refrigerators.
Small inverters, less than 300 watts, usually have a car lighter type plug. Larger inverters will have wiring to connect to the battery terminals.
Modified sine wave inverters are for general use, but may cause buzzing in some audio equipment. Pure sine wave inverters produce alternating curent that more closely resembles the current from your household AC wall outlet. Pure sine wave inverters are recommended for more sensitive equipment.
For a good discussion of the difference between modified sine wave inverters and pure sine wave (or true sine wave) inverters check out this article from Xantrex:
Sine Wave vs. Modified Sine Wave: Which is better?