Pooled mining is a mining approach where groups of individual miners contribute to the generation of a block, and then split the block reward according the contributed processing power. Pooled mining effectively reduces the granularity of the block generation reward, spreading it out more smoothly over time among the group.
Bitcoin mining is competitive, you want to solve or “find” a block before anyone else’s miner does. Then you will get the block reward and transaction fees from the block. During the last 3 years we have seen an incredible amount of hashrate coming online which made it harder and harder to have enough hashrate personally to solve a block thus getting the payout. To compensate for this pool mining was developed.
What a mining pool does is accept connections from miners anywhere in the world (if applicable and some are private) and pool their hashrate together thus mining with a higher total hashrate. In doing this the variance or luck of finding block is increased to the positive by having a larger total hashrate in trying to process a block the fastest.
A share is awarded by the mining pool to the clients who present a valid proof of work of the same type as the proof of work that is used for creating blocks, but of lesser difficulty, so that it requires less time on average to generate.
The Pay-per-Share (PPS) approach is to offer an instant payout for each share that is solved. The payout is offered from the pool's existing balance and can therefore be withdrawn immediately, without waiting for a block to be solved or confirmed. The possibility of cheating the miners by the pool operator and by timing attacks is thus completely eliminated.
This method results in the least possible variance for miners while transferring all risk to the pool operator. The resulting possibility of loss for the server is offset by setting a payout lower than the full expected value.
PPLNS has a higher payout. PPLNS will give you wide fluctuations in your 24 hour payout, but for hardcore miners, the law of large numbers states you will earn more this way. This is for people trying to mine as fast as possible.