Time and distance are described as ratios.
Time is the ratio between events. Any measurement of time we use, is relative to another event. Today we define a second to be a specific number of radioactive events detected from a cesium atom. We use cesium radiation because whenever we measure it (relative to some other event) the result is very consistent.
An event, is some action that takes place over a distance, but distance, like time is also a ratio. Every measurement of distance we use is relative to the distance of something else. Today we define a meter as the time it takes for light to travel some fraction of a second. We use light, because wherever we measure it (in a vacuum), we get the same value.
So we are describing time and distance relative to constants we observe in nature.
If you take two cesium clocks, sync them at some point on earth, and then take one of the clocks for a journey where you go a significant fraction of the speed of light, and then bring the clock back, and compare the clocks, you will notice that the cesium clock that took the journey has recorded a fewer number of events. So you could say that time has slowed down as you approach the speed of light, but you could also say that the ratio between the speed of light and the rate of cesium radiation has changed simply because of the underlying mechanism of nature.
So my understanding is there is nothing mysterious about time, it is just the ratio of events we observe in nature. However what is mysterious is the underlying ratios and why they change in cases like the one I describe above.