Xubuntu Core is a slimmed down version of Xubuntu that doesn’t come with all the additional applications that the current Xubuntu desktop ISOs have. It essentially only ships Xfce and the basic look and feel of Xubuntu, so there will be no office suite, media players, etc, etc.
The obvious benefit is that this ISO (about 600MB) will be faster to download – especially interesting for those with limited connectivity – and fit on a CD, as well as only adding what you want.
I have been working on this for a couple releases now, and starting with Utopic it’s available as a task and metapackage. There are ISOs which I’ve built, and starting with Wily, the plan is to produce official Xubuntu release ISOs on Ubuntu infrastructure.
The goal of this is not to create a lightweight version of Xubuntu, but more targetted towards advanced users to give them a base to work off of. See also Appendix A of the Xubuntu docs.
Does this have anything to do with Snappy, Ubuntu Core, or Convergence?
Nope, not a dang thing.
The current official method is to download the mini.iso, install, and when prompted, install the 'Xubuntu minimal installation' task. If you’d prefer to wait until after the installer finishes to install the Xubuntu core task, you can simply type
sudo apt-get install xubuntu-core^ (don’t forget the caret!) and away it’ll go.
Of courses, if you won’t have internet during installation, or don’t want to mess with the mini.iso, tasks, and the Debian installer, you can install from the ISO I’ve produced on the downloads page.