Simplified explanation:
It works such the Vbe is always constant (aprox 0.7V for a reasonable Ibe, with -2mV/K TC), the V2=-5V is constant, and the R1 is constant.
The Ibe=(-5+Vbe)/R1 is therefore constant as well .
The transistor's Ice current Ice=beta*Ibe, where beta is the amplification factor (100-500), therefore Ice is constant, with "any" V1.
The Ice will flow through the R1 as well (I_R1=Ibe+Ice), thus increasing the voltage at R1. Increasing the voltage at R1 will cause decreasing the Ibe, however, that is why the Ice decreases as well. So it finds an equilibrium, where
0 = (Ice+Ibe)*R1 + Vbe - 5V