Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of fraud or third party interference. In order to achieve this, Ethereum uses a proof-of-stake consensus algorithm.
Under proof-of-stake, miners are not rewarded for validating blocks of transactions. Rather, they are chosen in a pseudorandom way by the protocol to validate blocks.
The probability of a miner being chosen to validate a block is proportional to the amount of ETH that the miner has staked—that is, the number of ETH that the miner has put up as collateral.
If a miner attempts to validate a block that contains invalid transactions, they will lose their entire stake. This provides an economic incentive for miners to only validate blocks that contain valid transactions.
The proof-of-stake algorithm used by Ethereum is called Casper. Casper is based on research by Vitalik Buterin, one of the co-founders of Ethereum.
Under Casper, miners are not rewarded for validating blocks of transactions.