Imagine a friend on a moving train throws a ball inside it while you are standing outside on the platform. Imagine further that the ball moves in the same direction as that of the train. In this case, the ball will seem to go faster from your point of view because the movement of the train adds to its velocity. You will also see the ball travel a larger distance, namely the distance it travels in the train plus the distance covered by the train itself. Now imagine that instead of a ball, your friend throws a photon, that is a particle of light. He can notably do that with torchlight. However, light is very peculiar: it has the same speed for everyone, irrespective of the point of view. So if the distance covered by the photon is larger from your point of view, it means the photon will take longer to cross it: what you see will be dilated in time compared to what your friend sees inside the train.
Actually, distances inside the train will also seem shorter to you. Both the time dilation and this additional length contraction result from the fact that the speed of light does not depend on the point of view. Instead, it is our perception of time and distance that depends on our point of view.
Picture Credit : Google
