On a standard diode they allow current to pass in one direction and blocks it in the other, a bit like a one way value on a water pipe. This is because they have a vary large reverse bias voltage.
Zener diodes have a unique feature where the reverse bias voltage is much lower than standard diodes. So the one way valve idea is like it blocks the water until it gets to a certain pressure and then allows the water to flow until the pressure drops back down to the threshold.
This is super useful in applications where you want to regulate a signal to a particular voltage.
We use Zener diodes in the Microcontroller Education Board on the power input LED. So regardless of what voltage you put on the input, the LED will only see a maximum of 5.2 Volts.
These diodes are the 1N4733 which have a reverse bias voltage threshold of 5.1 Volts. So only allow current to flow through it when the voltage is above 5.1 Volts.
So if you connected this diode between a signal and ground, then if the signal goes above 5.1 Volts, it would open and allow current to flow through it, which would then regulate that signal at 5.1 Volts. Clever stuff.