It depends on the desktop environment. Most desktop environments provide a way to extend the desktop with extensions which can be written in various languages. In the case of Cinnamon for Linux Mint, being based on Gnome, it uses JavaScript to extend the desktop with extensions, applets (extensions that display on the menu bar), and desklets (extensions that display on the desktop). In fact, a good portion of Cinnamon[1] is actually written in JavaScript.
[1]: https://github.com/linuxmint/cinnamon