Debian is a Linux distribution on which many other distributions (such as Ubuntu) are based. It uses GNOME as a desktop environment by default, but other desktops such as KDE, Xfce and E can also be used. For further information visit Wikipedia.
The current stable version is Debian 8 jessie, and the unstable version (with more up-to-date package versions) is called sid.
Many packages related to OpenStreetMap can be found in the official Debian repositories. The DebianGis project provides a list of the Debian GIS Openstreetmap packages.