How frequency is modulated in FM transmitter circuit
All 'FM' circuits of this type are horrible for beginners because the FM component is generated by parasitic effects in the transistor (Which are second order effects and not covered in beginner descriptions of transistors). You actually have to go quite a long way down the semiconductor physics rabbit hole to really understand why this sort of works. 

These circuits are also frustratingly poor FM transmitters and are picky about layout even by the standards of 100MHz electronics. 

C1 and C3 are bypass caps the serve to remove RF voltage difference from the points they connect. 

R2 provides both mic bias and biases the transistor to a somewhat reasonable operating point, R1 is the emitter load resistor necessary to limit current and develop a point to inject the feedback. 

The transistor is operated in a common base configuration with feedback into the emitter (a low impedance point).