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See some explanations here:
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The electret microphone picks up the sound, when powered with a
resistor connected to a voltage, outputs a small voltage waveform which is proportional to the sound pressure waves. That waveform is then used to control the frequency of an oscillator, which is initially tuned to an ''output carrier'' wave at high frequency. The frequency depends on the components used: inductors, capacitors and capacitance between the three terminals of the transistor in a more complex way.
The transistor is used to add a small quantity of energy to the resonant circuit on each cycle to keep it resonating. It resonates whether or not there is any input from the electret microphone.
The input waveform modifies the equivalent capacitance of the resonant circuit by changing the biasing of the transistor. This affects the frequency produced, since the resonant frequency is inversely proportional to the square root of the capacitance.
As effect this causes the frequency to vary from the fixed frequency by some small amount which depends on the input sound. This variation can be received and output by an FM receiver as sound.
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