Starting another OS to run parallel with another system

So at work we have a few systems running on their own hardware that is identical to all of the systems. If one of the hardware fails, one of the running system will take over and start the system that failed, doing the work of both. All Linux and Intel cpu based. How would that be possible to have a OS start another OS to run together? It is not just running a program, it is running the entire thing as well. I have heard of things like how you can have windows let another OS use one of the cores on the cpu for parallel computing. But I am curious to how a system would immediately take over another system. It was super cool and my co workers unfortunately don't understand how it is done either.