Your battery will power your r-pod's lights, the water pump and the furnace fan, along with your propane detector. It will also power your antenna booster and 12v television (very few r-pods are equipped with a 12v television).
Technically, you can also run your fridge on battery, but it will drain the battery in a matter of hours. This mode is intended for use while you're towing your trailer and power is supplied from your vehicle's alternator. While dry camping, use propane mode on your fridge (note: the battery is needed while on propane mode to run the fridge's brain, but its a fairly insignificant amount).
Outlets will not work on battery power. Someone will likely point out that you can add an inverter to provide 120v power, but please research this fully before investing money as you'll find that a lot of things (coffee makers, heaters, hair dryers, toasters, microwave) will deplete your battery in a matter of minutes or hours.
-edit-
I should add that your battery also supplies power to your water heater - but, just for the DSI (automatic spark to light propane). Like your fridge, use propane for hot water when dry camping.