I have tried to understand this concept many times. I have stumbled upon an explanation that I think fits nicely, on a general level. I will use the rocket ship situation to explain. The mass of earth and the things on it creates a strong gravitational force where space-time is warped considerably. Because time is warped with space, it takes longer to get through time relative to a place with less gravitational pull and "straighter" time. A man on a rocket-ship moving extremely close to the speed of light would be moving farther and farther away from earth and feel its gravity less and less. The fast speed would limit the effect of gravity. Therefore, space-time, specifically time, would be less warped and straighter. So as this man on the rocket-ship moved through it, he would get through the time quicker than the man on earth gets through it. To move from one point in time to another in the straight line of space-time on the rocket-ship moving so incredibly fast is quicker than moving through a line of time that is crunched up and curved on earth. Therefore, the man in the rocket-ship gets to the "200 year later mark on earth" in say, only 2 and a half years. If he returns to earth, 200 years may have passed but for him it has only been 2 years. Summed up, the man on the rocket-ship is able to get to 200 years into the future on earth in only 2.5 years because time for him is straighter and takes less time to move through compared to earth. Can anybody with knowledge of this explain to me if I am on the right track?