The name self bias is coined because of the fact all the DC variations around Q-point tends to adjust itself in self bias circuit. The self bias circuit is shown below
All the capacitors shown in the figure acts as open circuit for DC and short circuit for AC signals. The self bias action can be explained as follows If Ic tends to increases due to increase in Ico (due to increase in temperature) the current through Re also increases. As a result voltage drop across Re also increases, hence base to emitter voltage decreases and base current decreases. Hence Ic increases less due to the action of self biasing resistor Re.
Stability factor S = 1 + (Rb/Re) Where Rb = (R1*R2)/(R1+R2)