A centralized exchange is a trading platform for digital assets that is operated by a centrally managed company. The vast majority of crypto exchanges are currently centralized exchanges, and they also generate the overwhelming majority of trading volume.
In contrast to decentralized exchanges, the user transfers his crypto-currencies to an external wallet that the exchange manages. The user is therefore not in permanent possession of his assets, which is why some people prefer to use decentralized exchanges.
In terms of trading volume, the largest centralized exchange currently is Binance.com. An overview of some exchanges can be found here.