What do people mean when they say that an engine has an interference design? How does it differ from a non-interference engine?
A piston engine is deemed to have an interference design if the normal regions of valve travel and piston travel overlap.
In such engines, collision (and damage) would occur if any of the valves is fully open and its corresponding piston is at the top-most point of travel (Top Dead Center) as they share the same physical space.
In contrast, the regions of valve travel and piston travel non-interference engine are physically distinct from one another, making valve-piston collision impossible.
The importance of valve timing
This lovely reddit post offers a layman's explanation using the animated GIF below:
Dude on the left is the piston, dude on the right is the valves. If the dude on the right gets out of step with the dude on the left he's in for a very bad time.
Correct valve timing is important in the grand scheme of any four-stroke engine's operation, but it is absolutely essential in preventing the valves and pistons from colliding in interference engines.
The engine's timing belt/chain maintains timing between the crankshaft and camshaft, which is why a snapped timing belt/chain can wreak havoc on an interference engine.
So why bother with interference engines? Isn't it risky?
I can think of at least two compelling reasons:
Higher compression ratio = Moar Power!
By making the valves and piston travels overlap the same physical space, the cylinder can squeeze the gases more, resulting in more useful work from any given air/fuel quantity.
Improved volumetric efficiency
Using interference design allows to extend the stroke of the valve as well, which helps with volumetric efficiency:
Superior breathing requires large valves that open deep into the combustion chamber, and high compression means a smaller-than-typical combustion chamber. This means the valves may need to extend into the area swept by the piston, and that's where interference may occur.
Timing belts/chains aren't exactly "regular" wear and tear items
In other words, the risk associated with a good timing belt failing is considered low enough for engine manufacturers to consider it a "risk worth taking".
A well-designed timing chain will usually last the lifetime of the engine. Timing belts will last at least 60,000 miles or so (recommended change intervals will vary between engines and manufacturers). Kevlar timing belts can last 100,000 miles.