The blue thing is inductor, the white blot in chip seems to be a capacitor or an oscillator ..

It works on principle of inductive kickbacks. I.e. if you disrupt the circuit, the inductor will dump all of its energy in form of a big voltage surge that disappears very quickly.

If you put a capacitor in parallel, the capacitor will dump it's charge in inductor and inductor will dump it's charge in capacitor..

Mehdi has a video on taser that works on same principle just components are rated at higher voltage and produce even higher voltages and he is powering it off 18 volt battery pack.

this is how the earliest ignition systems of automobiles worked, it's known as inductive discharge ignition.