In Call of Duty: Ghosts, the new Extinction mode is kind of like if you were to mix Zombies from Black Ops 2 and Survival from Spec Ops in Modern Warfare 3. In my opinion it’s one of the cooler new aspects in Call of Duty: Ghosts.
There are multiple ways to unlock Extinction Mode in Call of Duty: Ghosts.
How to Unlock Extinction Mode
Playing in the Campaign on Regular difficulty or higher, complete the first four missions. These should be Ghost Stories, Brave New World, No Man’s Land, and Struck Down.
Reach level 5 in any of the online Multiplayer modes