Use the Bootstrap classes named
hidden to hide/show different modules for desktop, tablet or mobile. These responsive utility classes are:
The screenshot is taken from the Bootstrap 2.3 official documentation, so please see the original source for the responsive utility classes documentation. Bootstrap 2.3 is the version that comes packed by default with Joomla! 3.x.
To use the visible and hidden classes, insert the name of the class inside the Module Class Suffix field inside the Advanced settings of the module:
For these classes to work, you need to insert a space before the name of the class (by pressing the spacebar key from your keyboard).