They don’t. Time dilation is a real, tested thing, but it’s something that you observe happening to *other* things and people – if you look at something/someone that’s moving very fast relative to you, you will measure time as passing slower for that thing/person than it is for you. BUT – time *as experienced by that thing/person* passes at the same speed as always.
The catch is that under some circumstances it’s possible (in sci-fi-like scenarios) for two people to start and end in the same frame of reference (so at rest relative to each other), and even together in the same room, but measure the time that has passed between the start and end as being very different. The so-called “twins paradox” is one. One of a pair of twins gets in a spaceship, heads off into space at near-lightspeed, turns around and comes back at the same sort of speed. During the trip each twin sees time as passing much slower for their sibling than it is for them. But (the “paradox”*) on their return the twin who did the trip (call them A) measures the elapsed time as much less than does the one who stayed (call them B). So from A’s perspective, B has aged very fast; from B’s perspective, A has aged very slowly. But note that, in each case, that’s someone *else’s* viewpoint. From their own perspectives, they’re each the age they ought to be.
*(It’s not actually a paradox because the experiences aren’t symmetric. B just stayed in one place, whereas A had to accelerate to get up to near-lightspeed relative to B, accelerate again to reverse direction and return, and accelerate a third time to stop – and that makes all the difference.)
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