>>126827231) Time and space are linked together. Agreed? This should be simple to accept. How far away is your job from your house? You probably say "30 minutes". You just used a time to report a distance. The coupling of time and space is ingrained into our brains.
2) When you move, you traverse at some speed. You cover some space within some time. Now imagine you travel from your house to work, at a speed of 30 mph. Your mom travels from your house to your work at a speed of 15 mph. You both traverse the same amount of distance, say, 15 miles. That spatial distance takes half the time to pass by as it does for your mom. We say the time has "dilated".
3) Actual time dilation says that when an observer is traveling at some speed, he measures the distance's traveling along to become contracted. Since time and space are linked (1) and since we need balance this contraction, we need to dilate (expand) time, in analog to (2).