The wiki article is a pretty good explanation. Basically, in Proof of Work a person/pool's chance of mining a block is determined by how much computing power they dedicate to the network. In Proof of Stake however, a person's chance of let's say "creating" a block is determined by their stake in the coin (how much they hold). This doesn't necessarily prevent centralisation but it does encourage re-investment in the cryptocurrency so that people don't cash out to fiat straight away. There are also hybrid systems like what Ethereum is starting to move towards for now.