A solar inverter converts the DC output from your solar panels stored in battery bank into a AC power that can be fed into all the commercial appliances in your home. An off-grid solar power system include a solar inverter with a PWM or MPPT charge controller, one or more solar panels and solar batteries.

In the context of solar+storage systems, a solar hybrid inverter is an inverter which can simultaneously manage inputs from both solar panels and a battery bank, charging batteries with either solar panels or the electricity grid or generators (depending on which is more economical or preferred).
Solar inverters comes with PWM charge controllers or MPPT charge controllers.

MPPT charge controllers are more efficient compared to PWM solar charge controllers. While single battery-single panel off-grid solar power systems can be configured using PWM charge controllers, more complex multi battery-multi panel systems configured using MPPT charge controllers will be far more efficient in generating power as compared to the same system using PWM charge controllers.