Both LightDM and GDM (GNOME Display Manager) are login managers.
They both provide graphical login capabilities (the GUI with the list of the system's users) as well as remote logins using the XDMCP protocol.
Ubuntu is supposed to officially replace GDM in favor of the lighter and more easily customizable LightDM
You can have both of them installed (or add even more, like KDM), but only one will be used at any time.
The default can be selected by running:
sudo dpkg-reconfigure gdm (if gdm is already installed)
More information on LightDM can be found on the Ubuntu wiki.