Interruptible operating systems are the operating system

Operating system

An operating system is a set of programs that manage computer hardware resources and provide common services for application software. The operating system is the most important type of system software in a computer system...

s with ability to handle multiple interrupt

Interrupt

In computing, an interrupt is an asynchronous signal indicating the need for attention or a synchronous event in software indicating the need for a change in execution....

s concurrently

Concurrency (computer science)

In computer science, concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other...

, 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.