Help me to understand the working of induction cooker circuit
C1 is a noise filter.

C3 forms a resonant circuit with L2.

L2 ("the main coil") runs on high frequency AC.  The MOSFET is not a simple DC switch.  It is driven by the controller with a high frequency square wave.  Popular Mechanics magazine says typical operating frequencies are in the 20 kHz - 75 kHz range.

https://www.popularmechanics.com/home/how-to/a5965/how-induction-stoves-work-elements-of-the-cooktop/

Yes, the impedance of L2 limits the current through it, but at 60 Hz that impedance is very low so the current can be very high.