EDIT: (for 14.04 when using Nemo Desktop to manage desktop icons for Ubuntu Unity)
As revealed in a followup comment, OP is using Nemo Desktop to manage desktop icons on the Unity Desktop instead of the default Nautilus Desktop for Gnome Shell and Unity (back in 2014. note that Nautilus Desktop no longer exists on 20.04+).
To prevent Nemo from managing the desktop icons, open the Startup Applications app and then disable Nemo Desktop from automatic startup.
It should be noted that newer versions of the Ubuntu Desktop and Gnome Shell now use a Gnome Shell extension to manage desktop icons and users will need to adjust the settings for the individual Gnome Shell Extension accordingly (assuming you are not using Nemo to manage desktop icons, of course). Of course this doesn't apply to the question as OP was using the Unity desktop, which was the default Ubuntu desktop in 2014.
20.04 and newer Ubuntu Unity Desktop (does not apply to Gnome Shell or the default Ubuntu Desktop!!!)
The following was tested on the Unity Desktop environment on 20.04 and should apply to newer versions like 22.04, 23.10, etc.
On newer versions of Ubuntu Unity, using Nemo Desktop to manage icons, we have a number of options.
Unity Tweak Tool
Installation (if needed):
sudo apt update
sudo apt install unity-tweak-tool
Open Unity Tweak Tool.
Select Desktop Icons.
- Select or unselect an item to display or hide the icon from your desktop view.
In the following screenshot, the selected items are highlighted in blue. The icon for each selected item will show on the desktop. Click on a selected item to unselect and hide it from the desktop.
Dconf Tool method:
If needed, install Dconf Editor:
sudo apt update
sudo apt install dconf-editor
Open the Dconf Editor app, click on "I'll be careful" and then navigate to org > nemo > desktop.
Toggle any "icon visible" related options on or off. To disable all icons, including Desktop directory files, toggle the "show desktop icons" option off (there is a note in 20.04 that this option is deprecated).
Lastly, you can always prevent Nemo Desktop from managing the desktop by opening the Startup Applications app and disabling Nemo Desktop.