What will knowing that data structure FB used will help you in anyway? If you have a problem of picking which data structure to use, then either post it here or compare the pro's and con's of each data structure and pick the one that best suites the problem. They don't use some magical data structure that no one knows. Most data structures are based on the basic ones like trees,arrays,list.... so get to know the fundamentals first.
Well, facebook is a social network, which has the word network in it, which usually implies a graph structure. And, coincidently enough, facebook uses a graph structure at its core, how surprising... I didn't need to look far to find that out, look at the wiki or the developers' page.