Transaction fees are a 'gift' from the person doing the transaction to the person that's processing the transaction. Processing transactions is done in blocks, and the process is called 'mining' because for every processed block, the person who processes the block gets 25 BTC (before today that was 50 BTC) plus the transaction fees. Obviously 25 BTC is a lot, which is why it's so hard to mine blocks. Mining is often done in groups, and the person who mines a block has to share the profits with the rest of that group.
IIRC the entire Bitcoin community mines 6 blocks per hour, and it's the mining process that keeps Bitcoin going, because without miners there couldn't be any transactions.
This is why transaction fees will increasingly be important as BTC matures, after all 21 Million are gone the only reward for "mining" will be the award of all transaction fees paid for transactions in that block, so much like the old west, mining is gradually replaced with banking/processing :-)
The reward for mining a block just halved; it'll continue to halve as the supply increases, so that 21 million is not the endpoint so much as it is an asymptote.
It will continue to halve, exactly one more time to 12.5, and then the next time after that, it will stop. Once the 12.5 reward is gone, the network will be supported entirely by transaction fees, and no new bitcoins will be created.
So, yes, asymptote, but the rest of your comment seems misleading. It will halve once more, that's not exactly "continue to halve."
I was also wondering how to reconcile this (seemingly very) early first halving with my concept of a 21 year bitcoin generation span. Thanks for clearing that up!
*edit: Turns out I was misinformed about the 21 year thing too. These projections have the halving terminating estimated at 2140. Don't suppose either of us will be around to see it.
And, actually, it may continue well beyond 2140. The only reason it would stop there is because the smallest value bitcoin can currently represent is 0.00000001 BTC (1e-8). Many people believe that the rising value of bitcoin will bring about a need to increase the number of decimal places that bitcoin supports. If this change is made to the protocol before 2140, the the mining reward will probably keep on halving to values even less than 1e-8 BTC.
I like it. Produce the proof that your rig solved the latest block, and you get your name in the book. Sounds much better than "no further rewards will be issued from this date."
Some people also wanted to make sure that their particular transaction was included in this block for posterity. Paying a fee increases the priority (https://en.bitcoin.it/wiki/Vocabulary) of the transaction to make it more likely to be included.
