How does a zener diode work in reverse bias?

Zener diodes operate like any other diode in reverse bias, they just have the point where they breakdown more carefully controlled, and usually lower than the typical ~50V for a standard silicon diode. The process by which most diodes (with breakdowns larger than a few volts) operate under reverse biases strong enough to cause breakdown is called "Avalanching".

Avalanching is where the reverse biasing is strong enough that the electric field between the positive and negative terminals grows to a point where the electrons and holes being swept across the junction have enough energy so that when they eventually release that energy it is enough to generate a new electron and hole pair which themselves are swept away by the electric field also.