Some Structure Groups in Tridion are displaying the "published" Icon
Can any one suggest why it is displaying the published icon for a Structure Group?
Because someone clicked the "Publish Structure Group information" checkbox in the publishing dialog.
Starting with Tridion 2011 you can publish information about the Structure Group itself to the Content Delivery tier. This could be used - for instance - to build navigation dynamically (not that I would ever recommend it).