The money comes from the effort of their mining and the value in the blocks they've mined. It's the same as when someone mine's gold -- the value comes from the effort of their mining and the rarity of gold. BitCoins don't need to be backed because they're scarce. You only need to back something that's not scarce. (That's why gold itself doesn't need to be backed.)
My poo is scarce. There is a limited supply of it produced over time. Therefore my poo is a valuable currency that need not be backed by anything.
Realistically, Bitcoins have value not because they are scarce, but because there is demand for them.
This demand is created because Bitcoins are cool, and you can have fun buying things with them, and playing with all the Bitcoin-related Web charts and the open source software and the crypto.
You could fork Bitcoin right now, and have your own identical system, and the coins in it would be just as rare and difficult to produce as Bitcoins are. They would also be worthless, unless you could make them cool, and make it possible for people to have fun doing things with them.
Bitcoins, like stocks, are a "psychological market." When stock is issued, the company gets its money from the initial sale, and no matter what happens to the stock value, the company never has to give the money back.
You can't do anything with the company, unless you have control, so for the average stock owner having less than 51%, the stock trades in its own little world, supported only by the belief that its value bears some relationship to the value of the company whose name is printed on the financial statement.
Bitcoins are like that. Should people ever become bored with Bitcoins, or not be able to do things with them they find satisfying, like thumb their nose at the government while buying Alpaca Socks, they will quickly become worthless.