Time dilation makes sense to me.
Yes, according to Einstein’s Relativity theory, a clock in motion will appear to tick out time more slowly than an identical stationary clock at your side.
General Relativity states that acceleration and the effects of gravity are ‘equivalent’. In other words, time appears to tick more slowly in strong gravitational fields (from an outside observer’s point of view).
In fact, it has been verified that a clock on the surface of the earth ticks out time more slowly than an identical one high above the surface (where gravity is weaker).
A similar effect occurs via spacetime stretching due to universal expansion. Gravity, in a sense, (also) causes spacetime to stretch. Time, according to a clock caught in a strong gravitational field, will appear to slow down, from an outside observer’s point of view.
GPS technology takes 2 of these effects into account.
1) the difference in time at the surface vs high above the surface where the satellites orbit.
2) the difference in time due to the high rate of speed of the satellite vs the ground (stationary).
Surprisingly, to me when I learned, is that, for GPS calculations, the effects of gravity win out over the high rate of motion. Each actually have opposing effects on time. ie, the ground-based person with the GPS device experiences more time dilation (due to gravity) tan the GPS satellite racing across the sky.