LMDE is a Linux Mint distribution, containing all of the nice Mint tools (installer, updater, menus and other utilities), plus lots of preloaded and preconfigured packages, but built on top of Debian GNU/Linux, rather than Ubuntu as the numbered/named Mint distributions (currently 14/Nadia).

via A look at Linux Mint Debian Edition (LMDE) 201303 | ZDNet.