The most significant use of DOCTYPE is to switch a browser between Quirks Mode and Standards Mode rendering.
This functionality came about because of the “broken” rendering in old versions of IE. It was realised that if Microsoft just “fixed” the IE rendering engine lots of existing sites would not render properly. So the way it works is if you put any valid DOCTYPE declaration at all in your page the assumption is that you know what you’re doing and your browser will render in a standards compliant way, and if you don’t put one in it will render in the old “wrong” way.
This was originally done in IE for the Mac, but this behaviour is the same in all versions of IE since IE5, and Firefox, Chrome, Safari and Opera.
What the DOCTYPE is supposed to be is a Document Type Definition. HTML is subset of SGML (as is XML). The DTD tells a parser which syntax you are using. So in a webpage your DOCTYPE should match the version of HTML you are using.