You can find inverters pretty quickly on Amazon, but you'll need to make sure that it is rated high enough to handle the appliance you're wanting to power. Since all inverters have a power rating, you'll just need to check the appliance and buy the appropriate inverter.
The basics are in desert_wanderer's post.
The solar panels collect energy.
The batteries store the energy.
The charge controller prevents the batteries from over charging, and make sure they get enough of a charge.
The inverter allows you to use standard household appliances running on 120VAC (the inverters allow you to convert DC stored in the batteries to AC, and allow the voltage conversion from 12V to 120VAC. If you are running direct DC appliances, you might be able to get away without this, but it depends on the voltage of the appliance, and how your batteries are wired. Battery banks can be wired for 6V, 12V, 24V, 36V, 48V, etc., but most are set up in a 12V fashion with an inverter (most of which run on 12V).