Using your processing power (GPU) to do a bunch of calculations to create a valid block of bitcoin transactions.  This rewards the person who did it with 50 bitcoins plus any transaction fees in the block.  It is quite a lengthy process, and the whole network (everyone mining) produces only on average about 6 blocks an hour.  If you mine in a "pool" you share your processing power with a bunch of other folks.  This can provide you a steadier income, as generating a block solo with only a GPU or two could take a very long time.