Giving it a shot - probably oversimplifying though:

MEVil happens when a miner has a front-run advantage vs a user. For example, if you post an on-chain transaction buying a variable amount of tether shittokens for a fixed amount of sats, where the algorithm decides the price (an automated market maker (AMM) contract), a miner can sandwich your transaction when they order the transactions in a block, to first make the price go up for you, and then balance it out. Making you get less shittokens for your precious sats.

The more often you can do this, the better, so there is supposed to be additional centralizing pressure coming from this: bigger pools find more blocks and thus have a better hold on the "decentralized" markets that way. This happened on Ethereum.

What this proposes is to create a market for people to keep their transactions secret, so that anyone can front-run a clueless AMM user by sharing some of their profits with the pools. Pools then include these secret transactions (that you cannot find in the mempool) in their blocks and everyone makes money - except of course the victim; that's why Matt coined it "MEVil".