Circuit analysis- boost controller IC frequency change
Circuits don't fall from the sky so next time please indicate where you found this circuit.

Q2 and Q3 with their surrounding components make an Astable Multivibrator. Go  here for an explanation on how such a circuit works.

Instead of resistors R2 and R3 being connected to Vcc as in a "normal" Astable Multivibrator, here they are connected to the emitter of Q1. Q1 just buffers (copies with a 0.7 V drop) the voltage across C1. The voltage across C1 is the voltage from the control input with some filtering.

That filtered and buffered control voltage is then used as the supply voltage of part of the Astable Multivibrator and that will influence the oscillation frequency as the voltage Vmid determines how fast the capacitors in the Astable Multivibrator can charge.