For nearly as long as we have had HTML, we have had trouble getting it to look the same in a web browsers.  Internet Explorer would display an element one while Netscape Navigator would display it a different way.  Usually, a compromise needed to be made to get your page to look similar in most web browsers.  Then CSS came along and really complicated everything.  Suddenly, different web browsers just wouldn't parse the code the same and it made trying to fix the problem very difficult for most web designers.  The good news was that once you figured out the compatibility for an element, it look 99.99% similar in all browsers.

What most web designers didn't know and what many still don't know is that if you specify the standard with which you wrote your HTML code, the browsers do a much better job of displaying the page the same way.  When you don't specify the standard, the browser uses its default rules for parsing the HTML.  Each browser uses different default rules which is why they display the pages differently.  If you specify the standard you used, the browser has to follow the rules for that standard!
When you specify your standard, you may find that coding techniques that you have always used in the past won't behave as you expect.  Likely, your code isn't optimized for that standard but it is likely that even though it didn't look that way you expected, most browsers display it the same which is a good thing.  You'll need to change your coding methods to suite the standard.  This is a little extra work now to eliminate trying to fix a compatibility problem later.