"Publish" is like completing the "Financial Report". It won't go to ATO or any third party. It is mainly for reporting purposes.

 "Published" is the same as "Lodged", once you press "Publish", the report will be locked.

To make a change, you need to press the lock icon, and the SFR is ready for any changes. 

Note that,  once the report is unlocked and if it was electronically signed, the e-signature will be canceled.

Related Article:

Financial Report - E Signature