It is like betting on a horse race, which I think most people understand, but just in case, I will first explain briefly how a standard peri-mutuel betting system operates at most horse tracks.
In a normal horse race scenario, you bet on which horse you think will win. The winnings that you receive are based on the "odds" which are calculated constantly, determined by how much money has been bet on each horse, from all of the bettors placing bets on that race. So, for example, say there is a 3-horse race, and all the winnings will be paid out to bettors (in real life, there would be more horses, and the event organizer would take a cut). $100 have been bet on Horse A to win, $20 have been bet on Horse B to win, $10 have been bet on Horse C to win. So $130 has been wagered in total. Most people think that Horse A will win, so there must be some reason for this, and it is probably likely that Horse A will win. So the payout if Horse A wins, is $130/100 = $1.3 per $1 wagered. So if you bet $1 on Horse A, and Horse A wins, you will receive $1.30 in winnings. If you bet on Horse B, and Horse B wins, you will receive $130/20 = $6.50 if you wagered $1. So you win much more money, but Horse B winning was much less likely. So the reward is always proportional to the risk, and the risk is determined by the knowledge of the market as a whole -- all of the people betting on that race.
Now, let's change things a bit. In a real horse race, all betting is closed when the race starts. So you can't watch half of the race, and go up and bet on the horse who's in the lead at that time. However, in this race, you can make bets during the race, and you can even change your bets during the race. So you're watching the race, and you see Horse B now has the lead, so you can change your bet from Horse A to Horse B. However, EVERYBODY will do this! The entire market will gradually change their bets to Horse B as the race progresses, and as Horse B is seen to be in the lead. By the time the race is over, everybody will have changed their bets to Horse B. Therefore everybody's payout will be the same, $130/130 = $1.00 exactly.
Now, you may say: What is the point of this? The whole fun of betting is to win something! Just getting your money back is boring! But if you were at a horse race, and you were given the option to change your bet in the middle of the race, wouldn't you take advantage of it? Wouldn't you at least NOT LOSE your money, even if it means it's not possible to win?
Ok, now what does this mean for BitUSD? It is a perpetual horse race, where you can change your bets at any given moment. The market converges on everybody "betting" that 1 BitUSD = 1 USD.
Now say that someone had a lot of BitUSD that they want to get rid of quickly. So maybe they put in an order for 1 BitUSD = 0.99 USD. There will be long a line of people waiting to buy the BitUSD's for the price of only 0.99 USD, because that will mean instant profit! And it also works the other way around. If someone has a lot of USD that they want to use to buy BitUSD, and they're in a hurry to do it, they'll come up and say "All right, gimme a bunch of BitUSD, and I'll pay 1.01 USD for each of them!" And again, there will be a long line of people happy to sell them BitUSD at 1.01 each, because hey, profit of 1 cent each!
As long as the market "agrees" that the price of 1 BitUSD = 1 USD, all of this will happen automatically. It is just like the market "agreeing" that Horse B is going to win the race, right before Horse B crosses the finish line.