Where do bitcoins come from? From the WeUseCoins.com video it appears they are just being produced by "miners" and sold to people. So who backs Bitcoin or gives it its value?
Although individual bitcoins enter the Bitcoin economy as miners are rewarded for processing transactions, it's much more helpful to think of all 21 million bitcoins as having been created when Satoshi Nakamoto defined the Bitcoin protocol and launched the Bitcoin network in 2009.
The reason for this is that the Bitcoin protocol specifically defines and controls when and how a limited total number of coins are rewarded to miners for the job of securing the Bitcoin network. These "bitcoins" are really just mathematical tokens which are very carefully controlled by the network protocol to prevent double-spending, counterfeiting, theft, etc.
By agreeing to use these mathematical tokens as money, the larger Bitcoin community is essentially "backing" their value and turning them into a currency in the same way traditional African and Asian societies used the money cowry despite the absence of any central bank. Unlike the money cowry:
Presumably, the members of the Bitcoin community who choose to accept them as money consider these features to be worth something, and value the bitcoin accordingly based on supply and demand on open currency exchanges.
Because bitcoins are given their value by the community, they don't need to be accepted by anyone else or backed by any authority to succeed. They are like a local currency except much, much more effective and local to the whole world.
So to sum up, bitcoins come from the Bitcoin community's agreement to follow a set protocol, and are backed by everyone who uses them as money.
The value comes from their scarcity. To use something as a medium of exchange, it only has to have a certain set of properties. Bitcoins have these properties, so they can be used as a medium of exchange.
They are fungible. That is, 10 bitcoins is 10 bitcoins. This makes Bitcoins more useful as a medium of exchange than, say, apples, which vary widely in quality, size, and so on.
They are scarce. The number of bitcoins is predictable over time.
They are easily transferred. They are not easily counterfeited.
That's pretty much all you need. Nothing needs to back them just like nothing backs gold. The primary purpose of a backing is to ensure scarcity. But the block generation algorithm does that for Bitcoins.
Bitcoins are just ledger entries. Like all modern currencies they are not backed by anything, but have value based only on their usefulness and their supply.
The addition of bitcoins into the money supply is controlled by the bitcoin software and is limited to a pre determined amount and rate of distribution.
The reason mining causes new bitcoins to be created is two-fold. On the one hand it's a mechanism to introduce bitcoins into the money supply that is controllable and essentially random (like winning little lotteries). On the other hand it motivates people to run the mining software which helps to secure the entire system.
The question is not very well worded, but I this article is the best response to the question of "What backs Bitcoins?"