Proof-of-Stake (PoS) is a consensus mechanism that allows blockchains to verify the transaction blocks in a more energy-efficient way than the mining process in Proof-of-Work blockchains.
The cryptocurrencies using PoS also being described as "green coins". Ethereum is on the move to PoS in their new version.
The way it works is that participants can lock their coins (staking) to contribute it to the blockchain. At a particular intervals, the protocol randomly assign the right to validate to one of the stake holders to validate the next block. Typically, the more coins you hold, the higher chance you get selected.
Once chosen, the validators are responsbile for the same thing as miners: ordering transactions and creating new blocks, checking and confirming blocks they don't create.