Compatibility View in IE8 basically renders the page as it would appear in IE7. IE8 is far more standards compliant than IE7, but pages designed for IE7 may not appear correctly using IE8 standards mode, thus compatibility mode was introduced to make the page fall-back to the IE7 way of rendering.
If you really want the detail of what is going on then read Just The Facts: Recap of Compatibility View from the IE MSDN blog.
Incidentally, if you hit F12 whilst using IE8 you will see the developer toolbar. At the top there are two options to change the document mode and the browser mode which will let you explore how a page appears using the compatibility view options.