The "Mozilla/4.0" reference is just there for historical purposes. After the word compatible it says MSIE 8.0, which indicates Internet Explorer 8 (your browser).
You can find out more about user agent strings for different browser versions here:
http://www.useragentstring.com/pages/useragentstring.phpHowever, if you are just generally trying to understand the types of browser people use when they visit your site, then as Adam says, use Google Analytics - it will be a lot less painful than sifting through user-agent strings by hand.