Subspace is the adventure mode in SSBB, or Subspace Emissary. There's a wiki for you if you need more info. Here is the SmashWiki link: http://www.ssbwiki.com/Adventure_Mode:_The_Subspace_Emissary.
The site is dormant, if I can say anything hope-inspiring. We all are having to move on with our busy lives, myself included. If I find it in me, I might restart Subspace.com, but that's how it stands and will likely stand.