The way it works is this: You go into an instance, say Naxx, and everyone knows ahead of time that it is a "GDKP run," or a "gold run," or a "cash run." You down the first boss, and Webbed Death drops. The master looter then takes bids of gold on the item (this can be done via public chat or via an addon), and whoever bids the most gold gets the item. The person who wins then pays that amount of gold (some raids have minimum bids of, say, 100g) to "the pot," and the raid moves on. Another boss drops, another item drops -- usually all items, including recipes and mats, are auctioned off -- and another high bid goes into "the pot." Then, at the end of the raid, the pot is evenly split among all members. Everybody who joined in on the raid gets an even share of the bidded gold, including people who got no items, or the Mr. Moneybags who won them all.
Interesting, no? It helps nearly every kind of character, from the people who don't need any of the gear but will willingly run instances for gold, to the people who don't have too much gear (newly 80 alts), but have plenty of gold to spend. And generally, the concepts of main spec or off-spec are completely ignored -- the item always just goes to the highest bidder. Anytime someone outbids you for an item, it just raises the amount of gold that you'll walk away with at the end, so theoretically, everybody wins.
There are issues, of course. Generally, because this kind of payoff attracts poorly geared but rich characters, raidleaders have to balance out who's in the raid, and if someone isn't pulling their weight, people are often asked to leave (if you suck, you get kicked, and can lose your pot). And of course, anytime gold becomes the only factor in getting gear, then you get into the point where people are encouraged to cheat and buy gold, not only breaking Blizzard's terms of service, but supporting the same system that's gotten so many players hacked in the past. It's naive to assume that everyone who shows up to a gold run with gobs of cash did so with money they earned themselves, so some players don't support this DKP system just for that reason.
Still, it's a fascinating, completely player-created idea, and especially when you're running with people you can trust and who have handled these raids before (generally, you want to go on a raid with someone who knows what they're doing, and fortunately, "good" GDKP raidleaders tend to get reputations for doing it right), there's a lot of potential to either pick up some nice gear or make a lot of money/badges/etc. We'll have to keep an eye on GDKP in the future (and Blizzard will probably do the same), because it's definitely growing in popularity -- odds are that there's a regular GDKP run on your server already, if not very soon.