The inverter produces 120V power from the 12V power from the batteries for powering whatever sorts of 120V devices you want to power when not connected to shore power. (Obviously there are limitations on how much power is available from an inverter.) Common examples include 120V televisions and other entertainment devices, laptops, crock pots, and maybe limited microwaving if the inverter and battery bank are sufficiently large.
As to why the 120V power to the fridge was cut, your guess may be as good as mine. Possibly there was some fault in the fridge or in the outlet it plugs into (water got into the outlet maybe).
