The basic working is this,

you give a SEPA transfer order to your bank in the afternoon.

Your bank consolidates all the transfers for the day in a big XML file and puts it in an ftp server in the evening.

Bundesbank pull it from there and puts the XML file in other banks ftp server.

Other bank pull it from there and completes the transaction.

In case the account does not exist or something happens the whole thing has to happen again to get your money back.

This is similar to BACS in UK.

Man the EU really needs to mandate compliance with SEPA Instant. Quite tragic that three years later and customers are still waiting on batch processes. FPS really is lush.