It all has to do with how new coins are generated and how transactions are verified. Proof of work has miners solving increasingly difficult math problems and verified transactions through this process. The first miner to complete the block gets the coins for that work issued to them and the block is added to the block chain.
Proof of Stake has basically people who hold the currency getting the new coins issued to them based on the amount of coins they have.
It all has to do with how new coins are generated and how transactions are verified. Proof of work has miners solving increasingly difficult math problems and verified transactions through this process. The first miner to complete the block gets the coins for that work issued to them and the block is added to the block chain.
Proof of Stake has basically people who hold the currency getting the new coins issued to them based on the amount of coins they have.