Your operating system is your software layer that acts as an interface between the hardware and your software applications. The operating system is the first layer of contact between you the user and your system hardware once you get beyond the virtually invisible to you boot micro code that runs when you turn on your computer. This interface seemingly makes the hardware differences between OEM hardware almost invisible to non-existent.
This code allows the many different manufacturers to run the same software package as their competitors.
Once your operating system has loaded, now the computer needs things to do. Normally every type operation that is to be done requires some sort of program code which has to be loaded. Operations such as word processing, spreadsheets, databases and many other programs are called applications and they run one layer above the operating system.
These software packages are optional to the required software for your system to load and be functional.
Your hardware is your physical devices needed to make your system work in the required manner that you need for it to work. Certain devices are basic and required in order to get a successful boot up. Such devices as a boot device, memory, a video display and keyboard are the essentials along with the necessary power cords and data cables.
Once these devices are in place and properly working, you can successfully boot your system and at least come to a dos screen.
I didn't mention a mouse because it 's not needed to boot into dos.
Some locations require the ability to communicate with other systems in their own little world which we shall for the sake of accuracy call a 'domain'. A domain is a group of computers gathered under a common network protocol and physically tied together in some form of network fashion and given a common name. Usually a server is involved which grants certain privileges and accesses according to the local security policies created in that domain.
When a sever isn't involved it's usually classified as a workgroup, but still all members will wear the same name of the workgroup.
This entire process whether it's a domain or a workgroup is called a network. Basically it's a group of computers and other devices tied together on a common bus.