Mining is the process of spending computation power to secure Bitcoin/Alt Coin transactions against reversal and introducing new Bitcoins to the system.

Technically speaking, mining is the calculation of a hash of the a block header, which includes among other things a reference to the previous block, a hash of a set of transactions and a nonce. If the hash value is found to be less than the current target (which is inversely proportional to the difficulty), a new block is formed and the miner gets the newly generated Bitcoins (25 per block at current levels). If the hash is not less than the current target, a new nonce is tried, and a new hash is calculated. This is done millions of times per second by each miner.