Trading on centralized cryptocurrency exchanges requires two counterparties to deposit assets with the exchange. The Exchange then manages the trade on a database and assigns the trade back to the counterparts. During this time neither counterparty controls their assets until the assets are withdrawn to an address or bank account they control.
This presents both a significant security vulnerability, presents a counterparty risk, and is fraught with delays. The settlement process is centralized and managed by an intermediary.
In decentralized settlement, the transfer of assets is atomic. As soon as authorizations from both counterparties are received, the assets are transferred directly, enabling counterparties to trade from self-custody securely, with no counterparty risk and no settlement delay.