Data is recorded in the Bitcoin protocol through "blocks". Blocks are records of the most recent Bitcoin transactions that have not been recorded in previous blocks (think of a stock transaction ledger). When you mine a block, there is a difficult mathematical puzzle to solve-each block has unique solutions. It uses the Hashcash proof-of-work system, which is used to limit email spam and denial of service attacks. When you solve the puzzle, you get rewarded with Bitcoins. The amount of bitcoins rewarded halves every 210,000 blocks, or four years. The reward for solving the puzzle will be the first transaction recorded in each block. Additionally, each newly mined block will have a reference (or hash) to the previous block to ensure it was mined legitimately, and is added to the end of the record of all blocks, which is known as the block chain. The block chain is the database of all Bitcoin transactions and is Bitcoin's main innovation. It serves to limit spending Bitcoins twice.
A bitcoin is divisible to 8 decimal places. Once the reward for Bitcoins becomes 0.00000001, it turns into 0 when halved and no more Bitcoins will be produced. This will happen when block 6,929,999 is mined, which should happen in the year 2140. Right now there are about 224,300 blocks, and a new block is added to the block chain every 10 minutes or so. Blocks will continue to be generated without end as long as people are trading Bitcoins, since it's the record of all transactions. If you go onto Black Market Reloaded and buy some Adderall because MSP doesn't cover it, that transaction of Bitcoins will be added to the block record.
Computational power is used to mine bitcoins. You can use CPU or GPU power to mine them, with a specialized program. Unfortunately, the amount of processing power needed, combined with the cost of electricity for home miners, makes it extremely difficult to turn a profit.
For an explanation in plain English:
http://codinginmysleep.com/bitcoin-m...-plain-english