A centralized exchange is one which is designed to be easy to use and access and often comes with additional trading features such as margin trading. However, the key difference is that they rely on a third-party service. This is very much like a bank for cryptocurrencies, which comes with its problems, such as hacks and bankruptcy; it is also something that is counterintuitive to the cryptocurrency culture.
A decentralized exchange has no third-party service to hold users’ funds. Rather the trades occur directly between people (peer-to-peer). This leaves the user in full control of their funds, leaves them more anonymous and makes it near impossible to be hacked.
Finding a decentralized exchange requires a bit of work, but they can be most easily identified if the exchange provides you with your private key. Your private key for your crypto wallet indicates that only you are in charge of your funds and you are not dealing with a third-party service which has control of your money.