Here's a wikipedia article of POS:
https://en.wikipedia.org/wiki/Proof-of-stakeI personally can't go much into detail. But CLAM for example is an example of a POS coin. You can basically stake your existing coins by holding them in a wallet (in the case of clam).
EDIT: After taking a little read myself staking coins is basically proving ownership of a certain amount of coins. This is an alternative POW where a "prover" is using computational power.
Here's an article about POW:
https://en.bitcoin.it/wiki/Proof_of_workBitcoin is a proof-of-work coin where users validate transactions by running hashing algorithms etc.
I suppose you'll get much more detailed information from a bunch of users around here...