Maximal extractable value (MEV) is a measure of the total value or profit available for extraction. MEV can be extracted permissionlessly by privileged protocol actors from the reordering, inclusion, or censoring of transactions within a block being produced on a blockchain. These privileged actors include miners, validators, and traders. MEV was formerly referred to as Miner Extractable Value but as Ethereum completes the transition to proof-of-stake, the term will be outdated. Validators will have the responsibility that miners once had, so the naming was changed while maintaining the same acronym. 
At this moment, Ethereum uses a Proof of Work (PoW) protocol where a group of people called “miners” play a big part in securing the network and validating transactions on the blockchain.
These miners are in charge of selecting and aggregating transactions into blocks, giving them the ability to decide which transactions from the mempool, the place where pending transactions rest until they are mined, they will include in these mined blocks.
This protocol doesn't hold back miners with any rules in regards to following this specific process. Miners have a lot of flexibility and can weaponize their power to manipulate transactions, thus pulling additional profits from users. This makes an “irregular” stream of revenue for miners, commonly known as miner extractable value or MEV.
How MEV works
Front-runners look through submitted transactions, always looking to find arbitrage opportunities that have the highest potential ROI. These front-runners pay the miners increased gas fees for the same transaction to benefit from arbitraging — of course, the miners select those transactions which have the highest gas fees assigned to them.
A user places an order for 10 ETH on a DEX, with each ETH token equating to 1,000 USDT — therefore, the total transaction amount equals 10,000 USDT. The user’s order will increase the price by a certain amount, and the miner can execute the order that falls in front of that specific transaction. This refers to front-running, as mentioned before.
The miner does this because they know that the traders’ order will bump the token price higher. Once the user’s order is executed, the miner creates an additional transaction that immediately precedes it, to sell the token after the trader’s order bumps up the price. To successfully front-run a transaction, bots peruse the Ethereum network for high-value orders and then execute new transactions so that they’re mined first are used.
This entire process allows these miners to sell their coins for a profit before the original trade is executed. It’s a highly efficient way to lock in large profit opportunities with low risk, making it highly attractive amongst miners everywhere.
In summary, once a transaction enters the mempool, miners can front-run the transaction and pass on a higher token price to the user, leveraging their power as miners to sequence transactions within blocks as they please. Additionally, the arbitrage or front-running bots can also spot MEV opportunities and capture them by “bribing” miners with exorbitant transaction fees to get their transactions executed in the specific order they please.
This shows the concept of MEV. While it may present fantastic opportunities for miners and arbitrageurs, there are inherent issues that the average retail investor suffers from as a result.
Problems with MEV
A major problem with MEV is that it often disincentivizes DeFi traders to execute transactions and exchange tokens on DEXs because miners can extract a hefty portion of their overall trade. Even worse, many DeFi traders are completely unaware of this problem. MEV also undermines Ethereum as a protocol given that it comprises the certitude and permanence of blockchain transactions. More than $600 million of value has been extracted from traders through MEV in 2021 alone. While DeFi and crypto have their benefits over traditional finance, they open the door to what could be considered deceptive practices. However, it can be fair to say that miners and arbitrageurs are simply taking advantage of the system that’s been put in place while maintaining the network that’s been put forth. In essence, MEV is the hidden tax on users that miners put in their pockets.
MEV can also be done on many other chains than Ethereum (Solana, AVAX, Binance Smart Chain, etc)
MEV might soon be unusable as Ethereum will soon switch from Proof of Work (PoW) to Proof of Stake (PoS). Since MEV is mostly done by validators who stake their ETH, if any validator tries to commit fraudulent activity, the validator's stake will be slashed, meaning some of the staked eth (or rewards) will be subtracted from the validator's stake.
Cowswap is a MEV resistant DEX. Instead of submitting swap transactions themselves users instead sign authorizations for Cowswap to make trades on their behalf within a specific price range and timeframe. Since these transactions dont appear in the public mempools they are not able to be exploited by frontrunners or sandwich bots. Additionally cowswap lets users pay with the token they are trading (i.e. DAI) instead of the networks base currency (i.e. ETH).
Flashbots is a research and development organization working on mitigating the negative externalities of Maximal Extractable Value (MEV) extraction techniques and avoiding the existential risks MEV could cause to stateful blockchains like Ethereum. Their focus is to enable a permissionless, transparent, and fair ecosystem for MEV extraction. This falls under three goals: Bringing Transparency to MEV Activity, Democratizing Access to MEV Revenue and Enabling Fair Redistribution of MEV Revenue.