Compatibility mode was introduced in recent versions of Internet Explorer. The newer versions of Internet Explorer work differently than the earlier versions so some web pages that worked fine in older versions do not display correctly in newer versions.
By going in Compatibility mode Internet Explorer looks at the pages as older versions did. However you will get warnings on newer pages that they will not display right since you are in compatibility mode and IE can not use newer features they may be using.
In some versions of Internet Explorer it is easy to turn Compatibility Mode on and off by using a button that looks like a torn piece of paper by where you type in Internet addresses. My problem with the button is that it is hard to tell if Compatibility Mode is turned on or off.
Another way to turn it on or off (whether button appears or not) is to go to the Tools menu. Then click Compatibility Mode. If there is a check by it then it is on. You can also go in Compatibility Mode Settings in Tools and tell it what pages to automatically use Compatibility Mode.
If you do not see Tools menu in Internet Explorer then right click in the blank area by one of your tool bars in Internet Explorer (where the buttons are and you type addresses) and choose Menu Bar. The Menu Bar will now appear in the top area in Internet Explorer.