A grim trigger is essentially a trading technique where one party pushes the trade all the way to breakeven or even beyond. For example, in the context of on-chain arbitrage, when one keeper pushes the gas bidding war to such a price that no one will be able to profit anymore from a certain on-chain profit opportunity, we call that a grim trigger.
Example: On Uniswap 1 Eth costs $4000, but on Sushiswap 1 Eth costs $3900. This constitutes a $100 profit opportunity. If one of the arbitrageurs is willing to spent $100 or more on gas fees to capture that profit, they just grim triggered the on-chain profit opportunity because they've made it a losing trade for every profit seeker involved (except or the miner who collects all the gas fees).
For KeeperDAO, grim triggers are one strategy to disincentivize bad actors (e.g. a keeper) from participating in Priority Gas Auctions (see below for an explanation) that drive up gas prices and causes network congestion.
KeeperDAO wants to incentivize Keepers to work together in its trading pool, instead of competing with each other or with other trading pools on-chain. When anyone tries to frontrun the protocol, KeeperDAO can instantly overbid and kill the MEV so that the profit opportunity instantly disappears and the bad actors are left with a loss (the cost of their gas fees). KeeperDAO's philosophy is very simple: Either the MEV gets shared fairly among all the network participants, or there wont be any MEV at all.