What does examples.desktop do?

It is a location launcher. A desktop shortcut to a location.

The contents looks something like this:

[Desktop Entry]
Version=1.0
Type=Link
Name=Examples
Name[es]=Ejemplos
Name[fi]=Esimerkkejä
Name[fr]=Exemples
Comment=Example content for Ubuntu
Comment[es]=Contenido del ejemplo para Ubuntu
Comment[fi]=Esimerkkisisältöjä Ubuntulle
Comment[fr]=Contenu d'exemple pour Ubuntu
URL=file:///usr/share/example-content/
X-Ubuntu-Gettext-Domain=example-content

It just opens nautilus at /usr/share/example-content/

The example content directory is a show case of open source and free culture.

You can read more about example content here. You can learn more about .desktop files here.

It shows up as a shortcut to a folder in the Files manager (circled in red).

I find it annoying as well. It's just an example, you can delete it. You can also delete it from /etc/skel to prevent it from appearing for newly created users too:

sudo rm /etc/skel/examples.desktop

It is a shortcut to a folder called examples.It contains Ubuntu Free Culture Showcase and Case Studies.