How does a zener diode regulate a voltage?
From the same tutorial where you found the circuit, you should also be able to find a plot of the diode voltage vs. current characteristics (shown below).

Normal silicon diodes drop around 0.7V in the forward direction (but that can vary).  Just about every diode will conduct at a higher voltage in the reverse direction.  The voltage at which that happens is called the "reverse breakdown voltage.  That reverse breakdown voltage depends on how the diode is made.

A Zener diode is purposely made to have a controlled reverse breakdown voltage, and to be able to be operated continuously in reverse breakdown.  So if you shove current through a Zener diode backwards, it should hold a fairly constant voltage.