C1 charges through R2 and R1 until the charge is high enough to turn on Q1. This causes Q2 to turn on. The LED is now connected to +Vcc and GND through Q2 and R3, thus lighting the LED.
After this happens, C1 discharges through the base-emitter of Q1. This causes Q1 to turn off, which then switches Q2 off. Once Q2 is switched off, the LED doesn't light up. Then the cycle repeats as the capacitor charges.
R2 can be adjusted to speed or reduce the charge rate of C1, this allows the user to adjust the flashing rate because C1 governs the oscillations(On and off fucntions) of the transistors Q1 & Q2.
D1 prohibits current from flowing to GND before the current goes through R2, C1 and R3.
R3 protects the LED and Q2 from excessive current when Q2 is switched on by Q1.
I hope this makes sense.