Example.desktop it is a link to a folder containing some examples of what you can do with Ubuntu. I believe is similar to Sample folders of other legacy OS.
The Public folder is a container for files and contents you like to share with other users of the system.
The Template folder is the default container for your your documents templates (text, audio, spreadsheets, etc.). It is the one that is parsed by default when you right click Nautilus file manager and hover on the New Document menu item.