The twin paradox is this. You have two twins A and B. A decides to go on a long space journey to a distant star and back while B stays at home. From the point of view of B time passes slower for A(by time dilation) so when A returns A is younger than B.

The paradox comes about when you consider the same situation from the point of view of A. From A's point of view B is travelling away and back. Thus time passes slower for B according to A. Thus when they meet it should be B who is younger. So who is younger when they meet - A or B?

The resolution to this paradox is that while all inertial reference frames are equivalent everything is not relative. In particular A had to accelerate while moving away from the Earth and had to deccelerate when he(she) reached the distant star. Acceleration is not relative thus it is A who actually moved and it is A who will be younger.