As described in
This software provides an abstraction of the used apt repositories.
It allows you to easily manage your distribution and independent
software vendor software sources.
In practice that means it provides some useful scripts for adding and removing PPAs:
$ dpkg -L software-properties-common | grep 'bin/'
plus the DBUS backends to do the same via the Software and Updates GUI.
Without it, you would need to add and remove repositories (such as PPAs) manually by editing
/etc/apt/sources.list and/or any subsidiary files in