A converter (a.k.a. converter/charger) handles power and charging needs when connected to shore power:
For turning 12v into 110v see inverters.
OEM converters generally do a good job of providing 12v to the house. They can do this even if the battery is absent or dead. All the RVer has to check is if the converter Amperage rating is sufficient for present needs.
OEM converters are notoriously cheap and dumb (lacking smart charging functions). Since they are stuck at one voltage the manufacturer picks a compromise setpoint. If this is set too high or too low for your usage patterns it can damage lead-acid batteries (batterycide).
This compromise setpoint should coincide with standard float voltage (Vfloat) for your battery bank. Typically this would be 13.2v - 13.4v for converters that are always on the grid, and 13.8v for batteries that are cycled but get put back on grid charging regularly.1)
Aftermarket converters tend to be higher quality than OEM, but some are still “dumb” single-stage chargers. Higher-end aftermarket converters often have multistage charging built in, or available as an upgrade.2) Note that a “dumb” charger might be fine if you have solar power on the vehicle, as the solar charge controller is likely a “smart” charger.
Three converter makers are generally respected on the CRVL forum. In alphabetical order:
SternWake says he leans toward Progressive Dynamics “for the ability to choose stages, holding 14.4 for 4 hours at the press of a button”3)
“Dumb” converters output a single voltage and work fine when solar charging is present (see above). In this scenario the 12v power supply can is set to ~13.x voltages to provide “float” support while on shore power.
If loads are run off the converter in the daytime the converter will just be supporting the solar yield and can be rather small. If used at night the converter will be carrying the whole burdern should be sized to your expected loads (20A, 40A, whatever).
It is possible to build a DIY converter from a power supply and MPPT charge controller.