An automated market maker (AMM) is a protocol for the Decentralized Exchange (DEX) that prices assets through an algorithm, rather than using an order book like a traditional exchange.
AMMs allow you to trade at a certain exchange rate on a DEX without having to find a counterparty. Instead of having to find a neighbor who is willing to trade USD for Euro, or go to the airport currency exchange counter, the AMM allows you to exchange tokens freely.
AMMs allow people to trade tokens peer-to-peer through liquidity pools, which are token reserves secured by a smart contract. The more tokens available to trade, the lower the exchange fee to swap between the tokens.
To learn more about AMMs, see Automated Market Makers.