Mining pools allow miners to work cooperatively by aggregating hash power and fair distribution of rewards based on hash contribution. Mining pools can be effective for smaller players who cannot earn payouts meaningfully on their own or for medium/more prominent players who want more regularity and predictability to payouts.
Mining pools use a variety of calculations to determine the payout. These are most notable in how risk is shared between a pool operator and the pool's miners. In pools, works are recorded via submitting 'shares' that meet a valid work threshold. As the only way to generate these is to attempt to generate valid blocks, it works as an effective proxy measure of hashing power.