In the United States, a designated survivor (or designated successor) is an individual in the presidential line of succession, usually a member of the United States Cabinet, who is arranged to be at a physically distant, secure, and undisclosed location when the President and the country's other top leaders (e.g., Vice President and Cabinet members) are gathered at a single location, such as during State of the Union addresses and presidential inaugurations.
His role is to replace the President if a disaster takes place and all the people in charge are injured or killed.
Here is an interesting article from Time Magazine about this role in the US.
Check out this article if you want to see what it's like to be "the designated survivor" in the US!
The ABC News tv series entitled "Designated Survivor" centers on the man who has to replace the President after a catastrophe took place. You can watch the trailer below: