What, exactly, is an interference engine? It's a piston engine that uses a four-stroke system of internal combustion and a poor history of precise performance. See, some of these engines are designed in such a way that the pistons and valves are at risk of interfering with each other through inaccurately timed movements. Piston and valve collision can cause extensive damage to the engine: Thousands of pounds worth of damage.
This is where the timing belt comes into importance. A well-functioning belt will prevent the aforementioned collision from occurring, while a broken one will only help speed along the destruction of your engine. It's possible to minimise damage by not restarting your engine after your timing belt breaks, but it's not always feasible to do this. If you attempt to drive your car regardless, you will be inflicting further damage on your engine and will be lucky if you can manage to pull over off of the road. More often than not, you can expect your engine to die within moments of the timing belt breaking.
To prevent this from occurring, it's recommended that you change your timing belt every 145,000 to 160,000 km travelled. Stories abound of people who ignored this recommendation and ended up breaking their belts shortly after eclipsing the 160,000 kilometre mark. These cautionary tales often have one thing in common: The driver lamenting over having to pay a ridiculous sum of money to repair the damage.
So in short, your timing belt won't break quietly: It will take as much of the engine with it as it can.