A DEX exchange is a trading platform where users can buy, sell, and conduct direct transactions with other users. When they want to exchange cryptocurrencies at market value without the help of a centralised authority, traders use this type of trading platform.
Contrary to centralized exchanges like Coinbase, DEXs only swap cryptocurrency tokens for other cryptocurrency tokens, not fiat cash and cryptocurrency. You can exchange fiat for a cryptocurrency (and vice versa) or crypto-crypto pairs, such as some of your bitcoin for ETH, through a centralized exchange, or CEX. Additionally, you can frequently make more complex decisions, including placing limit orders or trading on margin. However, the exchange itself handles all of these transactions through a "order book" that determines the price for a certain cryptocurrency based on active buy and sell orders, much to how stock exchanges like Nasdaq do.
Typically, there is no intermediary who can control what happens in the ecosystem. Decentralized Exchanges frequently employ self-executing contracts, doing away with the requirement for a third party to keep the funds of various participants. In this kind of exchange, gas (transaction) fees are typically less expensive, and some of them don't charge withdrawal fees.