Interruptible operating system

Interruptible operating systems are the operating systems with ability to handle multiple interrupts concurrently, or in other words, which allow interrupts to be interrupted.

Concurrent interrupt handling essentially mean concurrent execution of kernel code and hence induces the additional complexity of concurrency control in accessing kernel datastructures.

To put it in more layman's terms, it means that you can stop any program that is already running. This is a feature on nearly all modern operating systems.