What Stephen said.
I find an analogy helps to understand what "change" is and how it works.
Say you want to buy a candy bar ($1) from a store. You open your wallet (fiat wallet) and inside there is a single $20 bill. What is the min amount you can pay? It isn't $1; you can't rip up 1/20th of the bill and give it to the cashier. You need to pay $20 and since you only owe $1, the cashier gives you back $19. In traditional fiat monetary systems only the central bank can (legally) produce new bills, so bills are in fixed denominations. Your transaction may look something like the following.
Inputs:
$20 bill
Outputs:
$1 bill to cashier
$10 bill to you
$5 bill to you
$1 bill to you
$1 bill to you
$1 bill to you
$1 bill to you
We do this everyday so we don't really think about how it works or the limitations. Now lets imagine for a second that some system existed which allowed the cashier (or anyone) to securely destroy any authentic fiat money (bills) and print replacements in arbitrary amounts, while preventing double spending, counterfeiting, and ensuring that at all times the amount of money created is exactly the same as the amount of money destroyed. Since new bills can be produced on demand there is no need to limited them to just $10s and $20s, one could produce a $18.94537208 bill or a $483,389.27 one if they wanted to. In that case your transaction may look like the following.
Inputs:
$20 bill - destroyed
Outputs:
$1 newly created bill to cashier
$19 newly created bill to you
This modified system is how bitcoin works. Rather than bills or notes the network tracks inputs and outputs. All inputs are a prior transactions outputs and the network ensures each output can only be used (spent) once. Spending is just creating a transaction. Your input is a prior unspent output and you can't spend part of it (like trying to spend half of a $20 bill). So you spend the full value of the input by sending some to the intended receipient and some back to yourself. Your wallet hides and abstracts this. It continually scans the blockchain looking for unspent outputs involving your addresses. When your wallet reports your balance is 130 BTC it means the collective value of all the unspent outputs assigned to address you have the private key for total 130 BTC. This is similar to someone saying they have $130 in their wallet, more than likely it isn't a single $130 unit but the collective sum of all the bills in the wallet total $130.
In the case of your transaction (
http://blockchain.info/tx/0a1c0b1ec0ac55a45b1555202daf2e08419648096f5bcc4267898d420dffef87 ) you took a 10.89 BTC unspent output and spent it. 10 BTC was directed to your friend, and 0.89 BTC directed to an address you control, the "change". You can't only spend 10.00 BTC out of a 10.89 BTC anymore than you can spend $1 out of a $20 bill. The entire 10.89 BTC unspent output of some prior transaction becomes the input of this new transaction and in the process produced two new unspent outputs which have a combined value of 10.89 BTC. The 10.89 BTC input is now "spent" and effectively destroyed because the network will prevent it from ever being spent again. Now value was lost or created because there are new unspent outputs which equal the value of they "destroyed" input.
As Stephen indicated, in this case the fee is zero but if there was a tx fee it would be the difference between the inputs and the outputs. (i.e. 10.89 BTC input and 10.88 BTC output = 0.01 BTC fee). When a miner solves the block all the inputs of all the transactions are added together and all the outputs added together. The difference is the fees in the block and that is added to the value of the coinbase transaction which has the miner's address.