I think what you have is an INVERTER. It converts 12vdc (battery) power to 120vac power, giving you a source for a small amount (300 watts) of 120v power when shore powwer or generator is not in use. It probably was provided to power your TV, so that you can watch tv without being plugged in or using the generator.
There are large inverters (more watts) that can run more things, e.g. a microwave, but they require a lot of battery power.
Try your TV without connecting to shore power or running the generator. If it works, it is permanently wired to the little inverter - that's a common set-up. If it doesn't work, look for a switch on the inverter to turn it on, or a switch on the TV power plug to switch it to the inverter source.
Your rig also has a power CONVERTER, which produces 12vdc power from 120vac shore/generator power. It is used to charge your batteries and supply 12v to lights and such while shore/generator power is available.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL