The electricity in your home is AC at 60Hz in North America or 50Hz elsewhere. It is a sine-wave.
An inverter uses the power from a huge battery to create 50Hz or 60Hz at the same voltage as the electricity in your home but the waveform can be a square-wave for a very cheap circuit and many electronic products won't work from it, or the waveform can be a modified sinewave that is a little more complicated but nearly all products work from it, or the waveform can be a pure sine-wave which is made with a complicated circuit.
The oscillator in the inverter creates the 50Hz or 60Hz.
If you use a sine-wave oscillator driving a linear power amplifier then the amplifier wastes a lot of power as heat. The battery current is double what a modern circuit would be.
A modern sine-wave inverter uses a high frequency voltage stepup circuit that has a tiny transformer and a rectifier to make high voltage DC. Then another high frequency high voltage circuit uses pulse-width-modulation to create a stepped sine-wave then a small high frequency filter smooths the steps into a pure sine-wave. The parts that operate at high frequency barely get warm because they switch on and off.