Transaction recording, or mining, is the process of adding transaction records to Bitcoin's journal of past transactions. This journal of past transactions is called the block chain as it is a chain of blocks. The block chain serves to confirm those transactions to the rest of the network as having taken place. Through this public journal, Bitcoin nodes can distinguish legitimate Bitcoin transactions from attempts to respend coins that have already been spent elsewhere.
Mining is intentionally designed to be resource-intensive and difficult. Individual blocks must contain a proof of work to be considered valid and this proof of work is always verified by other Bitcoin nodes.
Mining is so called because it resembles gold mining in the sense that it requires exertion and slowly yields new currency.
Bitcoin's public journal was started on January 3rd, 2009 at 18:15 UTC presumably by Satoshi Nakamoto. This page (block) is known as the genesis block. The first transaction recorded on the first page (block) was a single transaction paying the reward of 50 new Bitcoins to its creator.
Bitcoin mining is so called because the rate at which bitcoins are generated resembles the rate at which commodities like gold are mined from the ground. See Controlled Currency Supply.
The Computationally-Difficult Problem
Mining a block is difficult because the SHA-256 hash of a block's header must be lower than or equal to the target in order for the block to be accepted by the network. This problem can be simplified for explanation purposes: The hash of a block must start with a certain number of zeros. The probability of calculating a hash that starts with many zeros is very low, therefore many attempts must be made. In order to generate a new hash each round, a nonce is incremented. See Proof of work for more information.
The Difficulty Metric
The difficulty is the measure of how difficult it is to find a new block compared to the easiest it can ever be. It is recalculated every 2016 blocks to a value such that the previous 2016 blocks would have been generated in exactly two weeks had everyone been mining at this difficulty. This will yield, on average, one block every ten minutes. As more miners join, the rate of block creation will go up. As the rate of block generation goes up, the difficulty rises to compensate which will push the rate of block creation back down. Any blocks released by malicious miners that do not meet the required difficulty target will simply be rejected by everyone on the network and thus will be worthless.
When a block is discovered, the discoverer may award themselves a certain number of bitcoins, which is agreed-upon by everyone in the network. Currently this bounty is 50 bitcoins; this value will halve every 210,000 blocks. See Controlled Currency Supply.
Additionally, the miner is awarded the fees paid by users sending transactions. The fee is an incentive for the miner to include the transaction in their block. In the future, as the number of new bitcoins miners are allowed to create in each block dwindles, the fees will make up a much more important percentage of mining income.
Making a Profit
Users have used various types of hardware over time to mine blocks. Hardware specifications and performance statistics are detailed on the Mining Hardware Comparison page.
Early Bitcoin client versions allowed users to use their CPUs to mine. The advent of GPU mining made CPU mining financially unwise. The option was therefore removed from the Bitcoin client.
FPGA mining is a very efficient and fast way to mine, comparable to GPU mining and drastically outperforming CPU mining. FPGAs typically consume very small amounts of power with very high Mhash/w, making them more viable and efficient than GPU mining. See Mining Hardware Comparison for FPGA hardware specifications and statistics.
Mining in the Future
As mining a block became more and more difficult, individuals found that they were working for months without finding a block and receiving any reward for their mining efforts. Thus they started organizing themselves into pools so that they could share rewards more evenly. See Pooled mining and Comparison of mining pools.