The basic idea is that you would play a single-player game, and (through an internet connection) what you do in that game would influence the environment or economy of the same game on someone else's console. Nintendo gives several examples of how this would work, including the construction of housing in a neighborhood, oil supply and demand, and even gossip, without those pesky "other players" messing up your game. The patent mentions the fact that people who share the same friends list may be able to see each other (much like Fable III does), but other than that, it's not so much the other players you see, but only their effects on the game's world.
Does this sound like something you'd be interested in checking out, as an MMO fan? Let us know in the comments below.