Quirks mode is basically the proprietary way that a given browser did things before the standards were developed. Since many web pages were developed to work with those proprietary processes changing the way that the browser works to comply with the standards would have broken all of those pages. Since few if any of those pages used a DOCTYPE it was decided that pages without a doctype should continue to be processed the crappy old obsolete proprietary way (now known as quirks mode) while those with a DOCTYPE would use the standard way of doing things (and therefore be able to work properly on other browsers as well).
Unless your web page was written before 2000 and you haven't had time to update it yet there is no reason for still using quirks mode as all browsers since 2000 have allowed web pages to be created that follow the standards and which therefore work in more than one browser. As the market share that IE has is now constantly falling due to the huge number of security holes in IE6 and the fact that IE7 is still many years behind in implementing changes to the standards the number of people able to view pages using IE running in quirks mode is steadily falling. With my own web site IE users are now down below 2/3 and still falling. Unless Microsoft release IE8 very soon and have it at least up to the standards of Firefox 1.0 or Opera 7 in what it supports I expect to see IE users visiting my site go below 50% before much longer. (admittedly people visitng my site are a bit more knowledgeable about computers than the average users because they are at least aware that there are browsers other than IE).