The Join a Discussion section on the Home page uses the Home Mid Left widget area. You have the flexibility to configure this widget area to display the content you would like to show.
To configure this for your site like our theme demo go to Appearance –> Widgets.
Drag an (BuddyPress) Groups widget to the Home Mid Left widget area.
Note: This optional widget is part of the BuddyPress plugin. If you do not have this plugin installed on your site you will not see this widget and should either install and configure the plugin or display a different widget in this widget area.
See the screenshot below for the settings we have configured in this widget.