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Operating systems are the core software that runs on computers. In general, the OS's job is coordinate processes between the hardware and software components on a computer. I like to think of the OS as like a sandbox in which it has dimensions, but the primary purpose is to provide an environment in which other applications can run.
For Home use, the biggest OS vendors are: Windows, Apple, and Linux.
For Business use, the biggest OS vendors are: Windows, Linux and Unix.
Windows dominates most home users and most client computers in networks, but not so much on servers. Many networks have Windows Servers running services like Domain control, Internet hosting, DHCP servicing, ect., but many networks have Linux or Unix boxes running as the primary server with the same services.