Meier himself explains the general design goal of Civilization Network on the official Facebook page, and it's more or less all about cooperation with friends and family. That's not to say there's no competition either, but the biggest edge a social networking game has is similar to an MMO -- cooperation with other players.
We'll be watching this project closely, as the blending of MMO qualities with a series like Civilization is by far abnormal. The next piece of the puzzle is the game's business model, but as of yet there's been no announcement of how Firaxis plans on making any money with the game. You can watch for beta news on the game's official Facebook page, and we highly suggest it.