Core allows you to sync your data with Xero by first connecting to your Xero company file. The authentication and company selection process is handled by Xero, but Core provides the synchronization feature to initiate the data transfer.
You can access this feature from the main menu > Productivity Tools > Integrations. On the Integrated Products tab, select your accounting software, Xero, from the list and click Disconnect to disconnect with it (assuming you were already connected to it). Check the Core Help for details.