To 'publish' a Project/Topic/Challenge is to make it public and accessible to your players.
'Unpublishing' does not delete the Project/Topic/Challenge, but simply "takes it off the web". Hence, you will still be able to edit your Project/Topic/Challenge.
You can publish and unpublish your Project/Topic/Challenge any time you want.
The publish/unpublish button will be next to your Project/Topic/Challenge's description.