In the first Black Ops, Zombie Mode was designed as a part of the single player experience. You could play it alone or team up with three friends for four player co-op, and there were no competitive elements.
Black Ops 2 will see a return of Zombie Mode in its classic form, but unlike the first game, it's being built from the ground up as an addition to multiplayer and will even come with a few competitive modes.
One of the examples provided was a competitive zombie survival mode, in which two teams of four players play in a regular match and see who can survive the longest. The addition of such modes would open up a lot of room for the competitive community in Black Ops 2, well beyond that of its predecessors.
Zombie Wager matches were also mentioned as a possibility, with teams tasked to perform various objectives during zombie mode. Players could be tasked with killing the most zombies in the shortest amount of time, or surviving a non-stop horde the longest.
We will find out more in later months, I will edit if I find out more!