Capacitors in Inverters?

If the delivered primary AC voltage is lower than what you require, you can use a step up transformer as here shown. My guess for the capacitors is that they filter the harmonics a little. This is about the simplest low pass filter.

If the input to the inverter from the batteries is 110VDC, the highest AC RMS voltage you could get from it will be about 70VAC. The transformer would then be used to step it up to something useful. The caps, I'm not sure but either a harmonics issue as mentioned by dvmdsc or maybe just power factor correction.

The raw output of an inverter is trapezoidal, approaching a square wave and frequently has overshoot spikes on the leading edge of each positive and negative wave. The transformer obviously boosts the voltage, but it also serves as an inductive filter as do the two capacitors. The final output may not be a true sine wave, but it will be close and have little spiking, if any.

Have to be more careful. The capacitors provide capacitive filtering.

That is the simple low pass filter.

The out put wave form of the inverter circuit is like pulses, transformer and capacitor helps to get sin wave also it works as low pass filter and plays a partial role of isolation transformer

First and topmost purpose is to attain Electrical Isolation from the Inverter.

Second most is to get desired output voltage

the 3rd advantage is to convert trapezoidal to quosi-sinewave.

As for as capacitors connected in parallel to secondary is not clear.

It may be to further improve output waveform by making a tuned circuit at 50/ 60 Hz.