The blocking oscillator relies on the fact that a transformer has a magnetic core which can only store a limited amount of energy.
When the power is applied, the transistor starts to turn on, by the current through the base resistor, causing current to flow through the transformer. Current is induced in the feedback winding is connected to the base, causing the transistor to turn on harder. The current gradually increases through the transformer's primary winding, causing the magnetic flux in the core to increase. Once the core is saturated, the flux doesn't increase any more, so no more current can be induced in the feedback winding. The base current now falls, causing it to turn off more.