An interruptible operating system is an operating system 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.
It means that the system can stop any program that is already running. This is a feature on nearly all modern operating systems.
References
Interruptible operating system Wikipedia(Text) CC BY-SA