Such an exchange was created on blockchain technology. There are no servers where the funds are stored, instead the funds leave one address and are transferred to another almost instantly. On DEX platforms, each user has full control over their private keys - they are not stored on the exchange. DEX also provide near-total anonymity as they don't require extensive KYC to protect their users.
DEX generally provide access to a larger selection of coins to exchange than centralized exchanges (CEX).
One of the disadvantages of decentralized cryptocurrency exchanges is their limited functionality. They lack some useful options and are more suitable for exchanging funds than for trading.