Perhaps the value is the fact a central bank can't obliterate the value of the currency based on a whim, using a bunch of esoteric economic logic to justify such policies?
* transactions where the private key associated with a public key holding value authorizes an outgoing transfer of value.
In short, miners build up a log of all exchanges of currency. While you have to "sign" any payments you make so no-one can steal your money, miners can choose to ignore your payments, and not add them to the blockchain.
Now, if the mining power was spread among many people, someone would put your payments on the chain. However, we are currently in a situation where a very small number of groups (between 4 and 6, depending on when you check), control over 50% of all mining. If they went rogue they could, in principle, lock the account of anyone they like, stopping them spending any of their bitcoins.
The 4 top pools are chinese and amount to almost 40% of the latest blocks mined.