An operating system in simple terms is the software you use to access anything on your computer.
You could have a bunch of programs installed but with no way to access them, they are worthless. Your operating system is the middleman between you and the hardware of your computer. An operating system typically has a user interface that is easy to use so you can run programs and install or uninstall things from your hard drive. Graphical user interfaces have been around for a long time and are by far the easiest way to manage the operating system. Anyone who remembers DOS knows what it's like to try to do things without a graphical user interface.
Microsoft Windows is by far the most popular operating system of all time. It is very easy to use and even a 4 year old can open particular folders, connect to kid’s websites and play games with ease. The biggest competitor, of course, is Macintosh's OS X. Many people consider this to be superior to Windows for a variety of reasons but when you get down to the nitty gritty, they are very similar. Windows has the best support for games so if you are a gamer, Windows is the best choice by far.
In addition to these big 2, there are others that are becoming more and more popular. Linux is a great example. Linux is an open source operating system and has one advantage over the others. It's completely free! It isn't quite the best choice for new computer users because it has an amazing amount of options you can mess with.
For the novice computer user, Windows or OS X are the only real choices. As you get more and more familiar with how operating systems work, you might try out Linux or some of the smaller operating systems because it can be a lot of fun to mess with them.