To understand the significance of real time systems it's useful to look at two every day activities, one non-real time and one real time.

Most of the actions in day-to-day work on a PC are not time critical. Whether a document takes 1 second or 5 seconds to load into a word processor is not really significant. Similarly, the time taken to load a web page is not important as long as it doesn't take many minutes. In both these cases it's the end result that's more important and not the time taken.

Now compare this to the work that an engine management system (ECU) has to do when running your car engine. The ECU measures certain parameters such as air temperature, throttle position and exhaust gas composition before deciding how much fuel to inject into a cylinder and when to fire the spark plug. In this case it's absolutely critical that these calculations are done before the next cylinder is ready to fire. In this case being late with these calculations is as bad as being wrong and could result in damage to the engine.