Theory of relativity. Relative to what? If I properly understand relativity, time ticks faster for an object sitting still than for an object passing by.
So, in a universe with only two objects which have the same "age", object A is sitting still and object B is quickly approaching it, then we can assume that when object B stops, object B will be "younger" than object A. That works if you choose object A as your point of reference, but what if you choose object B as your point of reference? In that case, object A is the one moving and therefore will end up being "younger" than object B.
How is this possible? How does relativity account for this paradox?
 A: Notice that one of the observers has to stop and turn back in order to compare watches and hence feel an acceleration. Thus they are not symmetrical in this sense. That's why the observer, who experiences the acceleration would be younger. As Feynman puts this fact in his famous lectures:

This [twin paradox] is called a “paradox” only by the people who believe that the principle of relativity means that all motion is relative; they say, “Heh, heh, heh, from the point of view of Paul [the stationary observer], can’t we say that Peter[the moving observer] was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that both should be the same age when they meet.” But in order for them to come back together and make the comparison, Paul must either stop at the end of the trip and make a comparison of clocks or, more simply, he has to come back, and the one who comes back must be the man who was moving, and he knows this, because he had to turn around. When he turned around, all kinds of unusual things happened in his space ship—the rockets went off, things jammed up against one wall, and so on—while Peter felt nothing.
  So the way to state the rule is to say that the man who has felt the accelerations, who has seen things fall against the walls, and so on, is the one who would be the younger; that is the difference between them in an “absolute” sense, and it is certainly correct. 

A: Special relativity is define has either points A or B being motionless to a third point, even if neither observer at point A or B can define that third point.  Only after comparing stopwatches will the observers know which of them was at relative rest and which of them was in relative motion to the third point.  Can't define absolute rest...but the classic twin paradox tries to disproof relativity by not defining relative rest to a third point.      
