RV battery refer to battery that runs the ‘house’ part of the RV. It is a simple 12 V battery that runs the RV ceiling lights, RV refrigerator, Exhaust fans, RV water heater, RV water pump, and RV furnace.
As an RV renter in most cases you really do not need to worry about the RV battery before, during, or after the RV trip. Any well maintained RV will have a decent battery.
One situation where you may want to be careful is when you do not have access to any electricity outlet for extended period of time. E.g. if you are camping at a remote location ‘off the grid’ or perhaps in a Wal-mart parking lot.
In such cases an RV renter should verify with the RV owner that the RV battery is in a good condition and can be used for extended period of times during the RV rental duration.