This is where the money is, so it's worth understanding.
Many engines are what's called an interference engine. That means the valves and the pistons pass through the same space, just at different moments, kept apart only by perfect timing. The belt is what holds that timing.
If the belt snaps, the top of the engine stops but the bottom keeps spinning for a moment. The valves and pistons meet. They bend, break, and gouge each other. On an interference engine, a snapped belt often means bent valves, damaged pistons, and a repair bill in the thousands. Sometimes it's cheaper to fit a whole new engine.
On a non-interference engine, the valves and pistons never share space. If the belt breaks, the engine just stops. You get towed home and fit a new belt. No lasting damage.
The catch is that many modern engines are the interference type. Unless you know for sure yours isn't, treat a snapped belt as the expensive kind.
A timing belt is one of the cheapest parts to replace on time, and one of the most expensive to ignore.