GNOME is the GNU Network Object Model Environment, although that name is depreciated now.
GNOME was started in the 90s to provide a desktop environment for the GNU operating system. At the same time, GNU Harmony was started to provide an alternative for the then-proprietary Qt libraries used by the KDE desktop environment. This approach was designed to ensure there would be at least one functional free software desktop for the GNU OS.
GNOME 3 is the current release of GNOME, and is developed by Red Hat and the GNOME community.