P2 / M1

A operating system is a layer of control which allows the user to interface between the hardware and the software. The operating system is in charge of managing the computer and it allows the user to run software. 

There are many different operating systems available, but the most popular ones are windows, mac OS and Ubuntu linux. 

Most modern operating systems have a GUI and multitasking features. A GUI is is a graphic user interface and it it is what you see on your monitor, it allows you to easily access installed programs. Multitasking is when you run more than one program at a given time, early systems did not support this, so when you were running a text editor, for example. and wanted to change to painting software you would have to close the text editor in order to run the other piece of software.
Modern computers allow you to run almost limitless software at the same time as a result of large amounts of memory and powerful multi core cpus.

The two main types of operating systems are linux and windows (Mac osx is not included here since it is based on linux). 

software

linux is generally free as well as the software for it, however more software is written for windows than linux, especially games. windows will also have much more driver support for hardware such as graphics cards.

security

Linux's security is vastly superior to that of windows. 
It is not needed to run anti virus on a linux machine, however it is 100% needed on windows 7 or after a short time you will get virus problems. Windows makes use of a feature called UAC or user account control, this is designed to protect the user from making changes on the system which could possibly harm it. It is also intended to stop users from making changes that they do not have permission to do. Linux usually uses the sudo system, on a linux machine there is always a root user which has permission to make any changes to the system (also called admin). Most linux systems do not allow the user to actually log in as the root user to prevent a virus or infection from making use of that power. So you use the sudo command (super user do) to perfom administrative commands.

ease of use

Windows is generally better for average users, although there are some Linux distros such as ubuntu and mint which the average person with limited knowledge could use just fine. One problem is that a user of a linux system will have to use the command line at some point.

As far as tech support goes both are about even. There is lots of support for free for both systems on internet forums, possible more so for Linux. However windows does have much more professional support.