An interruptible operating system is a type of software that can respond to external signals or events. It allows programs to pause or stop when something unexpected happens and then resume or start again when that same thing stops happening. This is important because it prevents programs from becoming unstable or crashing when a program does something it shouldn't. Think of it like a traffic light: if the light turns yellow or red, all the cars have to stop, but if it turns green again, they can start going. A interruptible operating system works like this too, but instead of cars, it’s programs.