The Twin Paradox is a hypothetical situation which explains the idea of time dilation. The idea of time dilation is that time can be warped by motion. To fully understand this you must realize that time is not constant throughout the Universe. Any object in motion will cause spacetime to curve around it, making time flow slower around the object relative to an outside frame of reference. So, with this in mind imagine that there is a pair of twins standing on Earth. They are the same age. One boards a rocket that is capable of attaining extremely high speed and travels to our nearest star, Alpha Centari. To get there and back within his lifetime he must travel extremely fast, lets say near the speed of light (C). As he is traveling extremely fast his rocket curves spacetime. This causes time around him to flow extremely slowly relative to his twin on Earth. So, when the twin finally returns to Earth following his long journey he is surprised to find his twin many decades older than himself. Why is this? Well, because his rate of the flow of time slowed down while traveling at a high speed while his twins rate of time flow did not change at all since he remained on Earth. This is the twin paradox. It explains how one can travel to their future.