Your 120 volt outlets, television, air-conditioner, and microwave all need a form of 120 volt power for them to operate. None of the above work off of the 12 volt battery, unless you have an inverter.....which you don't.
This may help in your understanding it all:
One of the most common questions and concerns I receive is about the RV electrical system. Most people ask if I can explain the RV electrical system in simple to understand terms. The electrical system in your RV can seem complex and confusing until you have a basic understanding of how it works. Your RV actually has three separate electrical systems. It has a 12-volt DC automotive system, a 12-volt DC coach system, and a 120 volt AC coach system. We are primarily concerned with the 12-volt DC and 120 volt AC coach systems.
The majority of campgrounds you go to will provide you with an external 120 volt electric source to plug into. Your RV has a heavy-duty power cord that is normally about 25 feet long. Depending on the type of RV you have, or purchase, it will either be a 30 Amp or 50 Amp system. When you plug into the proper campground electrical source it will supply power throughout your RV. You must have a 120 Volt AC power source if you are going to use the microwave, roof air conditioner, the refrigerator in the electric mode and the 120 Volt electrical outlets.
For the most part everything else in the camper works off of 12-volt DC power. When you are plugged in at the campground a portion of the 120 volt AC current is converted to 12-volt DC current for the items in the RV that work off of 12 volts. Some of these items are the overhead lights, the furnace fan, and the fan over the range, the vent fan in the bathroom, the water pump, LP gas leak detector, stereo, and the refrigerator when it’s in the LP gas mode. If you look at the RV’s power distribution panel you will see circuit breakers like you have in your house for the 120-volt AC side, and automotive style blade fuses for the 12-volt DC side.
If you are not plugged into an external power source you can still use the 12-volt DC system if you have a 12-volt deep cycle marine battery on your unit. As long as the battery or batteries are charged you can use everything in the RV except the microwave, roof air conditioner, the refrigerator in the electric mode and the electrical outlets.
If you have a motorhome, or you’re going to purchase a motorhome, it will have a battery for the automotive system and an auxiliary battery for the coach system. The coach battery is charged whenever the motorhome is running; the generator is running, or when it’s plugged into an external electrical source.
I also will add to Mark's great article, that you also have to have a form of 120 volt AC power for the electric heating element side of your water heater to function (if equipped)......since it's usually plugged into a hidden outlet that you normally don't see.