If you wish to manually run the batch(es) for syncing data between Salesforce and Xero, you can go to the 'Xero Configuration' tab.
In the Setup tab, at the bottom, there are two buttons.
Pull from Xero
This button will sync the data of Contact/Account then Invoices then Credit Notes in Xero and update the corresponding Salesforce records.
Sync to Xero
This button will sync the data of the Accounts then the Invoices, then Credit Notes in Salesforce and update the corresponding, or create new, in Xero.