Mining pools are a collection of miners that work cooperatively to solve a block. Once a block is found the miners are paid out in proportion to the amount of work contributed. A common analogy for this is a room full of workings scratching off lottery scratch tickets. Once any one worker finds a winning ticket the proceeds are split amongst all contributors in proportion to the number of tickets that each as completed.
Mining pools quickly rose to prominence as hashing difficulty skyrocketed and individual mining became statistically impossible as a source of revenue. Pools allowed small miners to work together to continue to earn currency despite a rising difficulty.
Mining pools use a variety of calculations to determine payout. These are most notable in the way that risk is shared between a pool operator and the pools miners. In pools works is recorded via the submission of “shares” which represent near blocks. As the only way to generate these is to actually attempt to generate valid blocks it works as an effective proxy measure of hashing power.
Common payment schemes are:
Pay-per-share, where miners are paid out for each valid share submitted. The downside to this is that miners do not have an incentive to submit valid blocks and could withhold them as a form of sabotage. This also puts the entirely of the risk onto the pool operator and as such these pools typically carry higher fees.
Proportional, in this approach miners are paid out when a block is found in proportion to the number of shares submitted in that round. This requires the discovery of a block before payout for shares and distributes risk between the miners and pool operator.
Slush Approach, a score based payment system in which shares submitted earlier in a given round are weighted more heavily in payouts. The idea here is to incentive miners to stay with a particular pool instead of rapidly moving to wherever profits are highest or when a payout is expected.
Luke-Jr Approach, in this approach miners are only paid out at block generation for work submitted (as opposed to pay-per-share). However in other to save on transaction fees a minimum floor is applied before payouts are sent (originally as high as 1 BTC).