What can you tell me (in layman's terms) about fuel injection in diesel engines?
You need to do it, or it won't run. ;-)
Older diesels use a complex mechanical injection system. It's very reliable, but when it goes wrong, you might as well scrap the car (or the engine at least). Because it's mechanical, it'll keep injecting so long as the engine's turning over, even without the key on, so long as there's fuel pressure and the engine's turning over. And because diesels don't need a spark to ignite the fuel, that means they often keep running on for a bit after key-off until the fuel pressure's drained away.
Instead of injecting into a plenum chamber and then sucking the air-fuel mixture into the cylinder, modern engines (diesel and gasoline) use direct in-cylinder injection with electrically-controlled injectors driven from the engine controller electronics, under software control. It gives much better control of fuel delivery, which gives better control over emissions.