Yes, it is real.
You offer an amount of money say $50 for a two bed room in a three star hotel room in downtown Portland (for instance). You submit your bid. Then they will reply with a yes or a no as to if it was accepted. If they do accept it you are committed to buy it. If they decline you, don't get a room, you can try a different amount but you will have to change dates or location (so they system will not just let you bid up $5, $10, $20, until you get one that is accepted) or you can buy a room through their listings without "naming a price."
There is no catch. If your offer of a price is reasonable enough in their estimation to provide you with their services they will accept your offer. If the hotels rooms normally go for $100 and they are worried they might not sell all their room the night you are looking at then there is a reasonable chance they will accept. If their rooms normally go for $500, then most likely your $50 offer will not be worth their time to change the sheets for you and they will decline.