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What is Zener diode and why do we operate it in reverse-bias?

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A Zener diode is a special type of diode designed to reliably allow current to flow "backward" when a certain set reverse voltage, known as the Zener voltage, is reached. (Source: Wikipedia)
Uses
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Zener diodes are also used in surge protectors to limit transient voltage spikes.

They are used to generate low-power stabilized supply rails from a higher voltage and to provide reference voltages for circuits, especially stabilized power supplies. They are also used to protect circuits from overvoltage, especially electrostatic discharge.

Surge protectors: A surge protector (or spike suppressor, surge suppressor, surge diverter, surge protection device or transient voltage surge suppressor is an appliance or device intended to protect electrical devices from voltage spikes in alternating current circuits.

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As the voltage remains at the Zener breakdown voltage, we use Zener diodes for voltage regulation. We use them in voltage stabilizers and various other protection circuits. We also use them in clipping circuits and clamping circuits. They provide a low-cost solution for voltage regulation. (Source: Electrical4u)