Debian is a widely used free Linux distribution system developed by the group of volunteers from around the world called the Debian Project.
GNOME was originally a GNU/Linux desktop and GNOME now runs on most Unix-like operating systems as well.
Gnobian distributions focus on Debian instead of other GNU/Linux distributions and on the GNOME environment instead of KDE, Fluxbox or other desktop environments... In a Gnobian distribution, when you boot Debian it loads GNOME (gdm).