The Zener diode maintains a fixed voltage at the base of the transistor, regardless of the supply voltage. The supply voltage must be higher than the Zener voltage (plus the voltage drop across the 1k resistor). As a result, the voltage at the emitter will also be fixed, and equal to Vb-Vbe. This means the emitter current will be constant (fixed) since the 20 ohm resistor does not change. It's fun to change the value of the current limiting resistor or to change the Zener value.
