In ideal diodes the current can only flows from the anode to the cathode. This means if the anode is taken at a voltage higher than the cathode the current can flows (as in a closed switch) otherwise the circuit will be open and no current will pass. In real world diodes, instead, if the anode is taken at a voltage lower than the cathode (this is called reverse polarization) the circuit will be open (even if a small current will be present) until a voltage Vbkd called breakdown voltage where a sudden and deep conduction take place. This means that after Vbkd has reached small increases in voltage cause very high increases in current (so the voltage is almost constant while the current varies very much). In this case an effect called "avalanche" will destroy the junction.
In zener diodes the direct polarization is the same as in "normal" diode, but the reverse characteristic is made usable without the risk of the avalanche effect (under the specified conditions). The breakdown is here called Vz: zener voltage.
Placing then a zener diode in parallel (after a limiting resistor) to the source will have no effect until Vz has reached; after this point the current will start to flows into the diode while the voltage is kept to Vz.