Proof of stake mints new coins based on who already has coins (they have a stake in the platform's success). This is opposed to solving arbitrary math problems

Proof of stake mints new coins based on who already has coins (they have a stake in the platform's success). This is opposed to solving arbitrary math problems to mint new coins, which is called "proof of work". At some point in the future the Ethereum client will have the proof of work algo swapped out with the proof of stake algo.