By the default, elementary OS doesn't have a desktop folder—no files can be placed onto the wallpaper. Note that this isn't just that icons don't show, there really is no desktop folder:

Where should I store my files / folders which I normally have on my desktop?

Where can I place my links to start applications if not on the desktop?

If I'd still like to have an Ubuntu / Windows-like desktop, is it possible to install / activate it - and if so, how?