The CDC is an organization in-game. It stands for the Center for Disease Control and Prevention. The CDC issues gray news headlines, such as "1 out of every 5 Americans is overweight," and such, similar to what the WHO does in real life. Although they are supposed to find cures for diseases in real life, WHO performs this task in Plague Inc.
One of the reasons it is featured in the game is because the CDC is officially partnered with Plague Inc. in real life, thus adding news headlines to the game.
They also may hunt Patient Zero down. Note that they don't actually have any effect on the game unless they actually find Patient Zero. Preventing this unlocks the achievement Patient Who?.
One thing to note is that this achievement will not be attained if a Cheat Plague is being used.