DIR stands for "Doing It Right". It is a gear configuration and diving style used by many technical (cave, wreck, deep) divers today. The phrase was coined by a group of cave explorers called the Woodville Karst Plains Project, or WKPP. They are led by a man, who you either love or hate, named George Irvine. The gear style includes the use of a backplate and wings instead of a BC, using a 7foot hose for your primary regulator, a bungee necklace holding your backup regulator under your chin, donating your primary regultor to an out of air diver, and many other requirements on what type of gear used, and where you place the gear.
DIR is a very controversial subject. It has a very strict guideline on what you do, and how you dive. If you break from this, you are considered, by it's name, to be doing it wrong. DIR advocates feel that this is the safest, and only way to dive. Some will go as far as to say you are unsafe if you do not follow this style. However, that is a very small, but very vocal, portion of the DIR crowd. Unfortuneatly, as vocal as they are, they tarnish DIR in the eyes of the non-believers. If you want to see a good fight, get a vocal DIR advocate, and a vocal anti-DIR diver and put them together.
*Note* I do not consider myself DIR or anti-DIR. I feel there are many ways to dive safe, depending on the type of diving you are doing. I dive a DIR style rig, or modified Hogarthian, but do not preach it as the only way to dive. However, I do feel it is the safest for me and the diving I do, and makes the most sense for the style of diving I do, cave diving.
If you want to see how vocal DIR/anti-DIR can get, check out the following threads.
http://www.scubaboard.com/t8229/s.html
http://www.scubaboard.com/t8260/s.html
http://www.scubaboard.com/t8597/s.html