You should read up this to learn about difference between PoW and PoS (proof of stake) and how it should affect Ethereum. We still have to wait until end of year to see how it will exactly look like, but basically, you still "mine" or mint new ETH, but only with staking your owned ETH.
https://github.com/ethereum/wiki/wiki/Proof-of-Stake-FAQI have watched a video of an eth miner on youtube and he explained the PoS in a way that there will be no mining, actually. Because mining is about spending energy and getting rewarded for that. One proves that he has done some work. Proof of stake, on the other hand, is rather about holding eth, doing nothing except being a part of the system and confirmation of other eth being valid. I guess new coins will appear and be given to those who own a lot of ethereum.