In cryptocurrency a DEX is a Decentralized peer-to-peer Exchange. It is an exchange run by code that is not controlled by one entity. It is a place where people can trade cryptocurrencies directly without a middleman. On a DEX every transaction is generally written to the blockchain and a swap is fulfilled through trustless settlements called atomic swaps. The DEX replaces the need for a centralized exchange to act as a middleman.
Some examples of a DEX include BarterDEX, Idex, Crypto-Bridge, and Waves DEX.