The Quick Icon plugin group supplies the status tiles shown on the Home Dashboard, the first screen an administrator sees after logging in to the back end.
Their main job is notification. If an update is available for Joomla itself or for an installed extension, a Quick Icon plugin is what puts that in front of the administrator instead of leaving it to be discovered. Other plugins in the group report on the site's environment and configuration in the same place.
Each tile comes from a separate plugin, so any of them can be switched off. They are listed together under System → Plugins when the list is filtered by the quickicon type.