To the OP:
Asking, "What is DIR?" is like opening Pandora's box. You're going to get a bunch of links, a few reasonable answers, a lot of bizarre answers, and a lot of flack. A lot of the people who will answer you are not DIR divers and have not had any training from any legitimate DIR source.
DIR is a holistic approach to diving that grew out of a particular cave diving project in Florida. The essence of the equipment configuration is simple, streamlined, and efficient. If you don't need it, don't take it on the dive; if you do really need it, you may need two. Configure everything so that you minimize entanglement hazards and drag. Use a standardized setup so that everybody on the team knows everybody else's equipment inside and out -- They can spot errors before the dive, and they can handle problems during the dive.
Combine this equipment configuration with a set of standardized protocols for communication and procedures, and a standardized set of gases, so that everybody is on the same page for decompression on any given dive. Add a high standard of personal skills, so that every diver on the team is competent, confident, and cooperative. Make sure everybody goes through the same training sequence, so that all divers are on the same page.
That's DIR diving.
The DIR equipment configuration is pretty simple, and you can get a good written description off the GUE website (look at the equipment requirements for the classes) and a good visual off the BAUE site. The essence is this: A backplate and wing assembly for a BC. A long hose (5' or 7' in general) for your primary reg, routed around the back of your neck to your mouth. A backup regulator on a necklace, so it lies directly beneath your chin. A simple brass and glass SPG; a knife on the waist belt, a canister light, and fins with spring straps. You can get into more detail, and obsess over brands, and positions of gadgets, but the underlying principles are streamlining and standardization.
This thread will almost certainly degenerate into chaos; if you have any further questions about DIR diving or equipment, please feel free to PM me and I will answer questions with the best information I have. I am GUE Cave 1, so I have a little bit of authenticity in answering.