Many people hear about Bitcoin mining and wonder what it's all about. One question is who can mine? The answer is anybody with a computer. There is an entire section devoted to mining at the Bitcoin forum. Anyone can start mining with freely available software, but competition is pretty high. For most it can be easier and cheaper to get bitcoins other ways, like working for them or buying them.
To use bitcoins you never have to worry about mining. However, a technical overview follows.
Mining serves two very critical functions for Bitcoin. One is validating transactions and the other is securing the nework. As long as Bitcoin exists there will need to be miners.
People have incentive to mine because of the "block reward" and transaction fees. The block reward is a special transaction in Bitcoin which gives new coins to the miner finding the block. The block reward started at 50 BTC and automatically halves about every 4 years so that over time there will only be 21 million bitcoins total. Once all coins are mined it's believed a large volume of transaction fees will provide incentive to continue mining. While nobody technically needs to pay transaction fees, doing so can prioritize confirmation on the network which many people value.
Mining involves using a computer to solve a complex math problem. The computer that solves it first "wins" the block meaning that miner can place the valid new transactions seen on the network into the block. If done correctly, as signified by other miners beginning work on the next block, that miner receives the block reward and any fees associated with the transactions to be included in the block. The difficulty of the problem is automatically adjusted so that no matter how many computers work on the problem the likelihood of solving it only occurs about every 10 minutes. This keeps the rate of new bitcoins coming into circulation relatively stable.