When power is first applied to the circuit the transistor is off. Current flows through the resistors which form a potential divider and into the base of the transistor via the feedback winding. This turns the transistor on.
The transistor turns on and current begins to flow through the primary coil, as this happens an EMF is induced into the secondary winding but no current can flow there since the flybacks internal diode blocks it.
As the current in the primary ramps up it also induces an EMF on the feedback winding which opposes the EMF from the potential divider, turning the transistor off.
When the transistor turns off the current in the primary coil is suddenly interrupted and large negative voltage spike appears across the primary, a stepped up voltage also appears on the output of the flybacks secondary coil.
But now there is nothing to keep the transistor off so the cycle repeats itself over and over.