An inverter is a central component of any alternative power system that requires alternating current power. Inverters transform low voltage 12-volt DC power to standard 120 / 240 volt AC current draws in modern appliances and tools. Inverters switch DC back and forth to make AC power, which is then filtered, and transformed and stepped up or down to match the desired waveform. More processing makes for a cleaner output with fewer voltage spikes, but reduces the overall efficiency of the process.
Modern inverters come in two basic types - modified sine wave and pure sine wave. A modified sine wave is close but not identical to the waveform that comes from your public utility. Modified sine wave inverters can run most household appliances including TV's, stereos, lighting, computers, etc. Pure sine wave inverters produce a waveform that is identical to and in some cases better than what you get from your public utility company.
Modified sine wave inverters do less processing of the power; this can cause some devices (laser printers, tools with variable speed motors, and similar items that need an abrupt pull on their power demands). Pure side wave inverters are more expensive, but won't cause "laser printer brown outs" or "table saw brown outs" when running off them. Because they do more processing of the power, they're less efficient overall.
When looking at inverters, of either type, they have two capacity ratings. One is the continuous output rating, the other is the surge capacity rating. Continuous output rating is how much power, in watts, the inverter can provide for hour after hour. Surge capacity rating is how much power the system can deliver for a short period of time. You'll need decent values for both – the continuous output rating limits how many devices you can have running at once; the surge limit is useful for appliances like refrigerators that need more power to start up than to keep going after they've started. Larger inverters (up to 10,000 watt monsters, useful for running a small building) are more expensive.
Your inverter need will be a function of the Watts used by your current appliance mix, multiplied by a fudge factor set by the total efficiency. You may want to oversize your inverter initially so that it can handle adding more appliances to your home, or so that you can utilize more capacity with your solar array as you add panels. This fudge factor is generally about a 15% surcharge; take the total wattage on your home, and multiply by 1.15 to get a good value for your load calculation worksheet.
Most inverters are 120 volts alternating current, but 240-volt alternating current inverters are available if you wish to run loads that require this. There are also step-up transformers available that attach to your 120-volt inverter that allow you to produce 240 volts alternating current, if necessary. In some cases you can also "stack" two similar 120-volt inverters together to provide 240 volts. Most inverters on the market also serve double duty as portable battery rechargers, which is a handy useful feature.
And, as with the advice on battery arrays, and solar panels, ALWAYS use the rated wiring. Don't get cheap here; this is a piece of gear that can cause house fires if the power cabling overheats.