Proof of stake. Instead of miners trying to make valid hashes, people bet their ether on which blocks will be accepted, and the blocks people bet on the most are the ones that get accepted. (That's Ethereum's PoS design anyway.)
In proof of work, the miners race each other to make blocks. Any time they spend actually validating transactions slows them down; they might find a block and not get their reward if another miner was a bit faster. The transaction fees have to be high enough to compensate for this risk. Since the reward goes up as the coin price goes up, the fees go up proportionally too.
In proof of stake, this race goes away. Blocks are released on a fixed time schedule. The fee no longer has to compensate for risk due to lost time, and instead just has to pay for actual computational cost of the transactions.
In proof of work, the miners race each other to make blocks. Any time they spend actually validating transactions slows them down; they might find a block and not get their reward if another miner was a bit faster. The transaction fees have to be high enough to compensate for this risk. Since the reward goes up as the coin price goes up, the fees go up proportionally too.
In proof of stake, this race goes away. Blocks are released on a fixed time schedule. The fee no longer has to compensate for risk due to lost time, and instead just has to pay for actual computational cost of the transactions.