Most of the essentials are designed to run off the battery (12V DC), like the lights
, water pump, DC outlets (cigarette lighter type) and fans, but not anything using 120V AC will not, like the duplex plugs and fridge
on AC, and if you have them, air conditioning
, electric water heater, microwave
and the like.
An inverter will transform 12V DC to 120V AC for use with 120V stuff, but depending upon what you use, would put a big draw on the battery and drain it rather fast.