Understanding this simple FM receiver
The inductor L, the capacitor C and multiple (intrinsic) capacitances of the transistors form an parallel LC-tank circuit with resonance frequency of about 100MHz. The trim-capacitor C allows tuning this LC-tank resonance frequency. 

Such a parallel LC-tank has its highest impedance at resonance frequency, thus it also has its highest voltage at resonance frequency. Every frequency deviation from resonance frequency leads to an amplitude change of the voltage at the left terminal of C1. This voltage is then coupled through C1 to the earphones. 

For the FM-demodulation to work, the LC-tank has to be tuned a bit off resonance, so that the radio works on the slope of the resonance curve and thus the change of frequency results in a (mostly) linear change of voltage (this technique is called slope demodulation).  

So in the end, this LC-tank acts like a (delta-) frequency to (delta-) voltage converter which is the basic function of an FM-receiver.