The problem is, humans are only hard-wired for local time. For hundreds of thousands of years, we have carried around with us the notion that it is the same time wherever we go, that it is noon when the sun is directly overhead. Few considered that, by this measure, everybody's noon was slightly different from each other's.
This human-based discrepancy only became a problem when technologies started bridging gaps between far-flung human communities. The railroad and the telegraph both forced people to reconcile, for the first time ever, that noon in New York occurs at a slightly different time than noon in Cleveland, or even in Atlanta.
Take the now seemingly short distance between Philadelphia and New York City, only about 100 miles apart. In the middle of the 19th century, it would take someone about 2 and 1/2 days to travel by horse, or stagecoach. So it did not really matter that noon in NYC was slightly different than noon in Philly.
Once the railroad was built however, that small difference was telling. The first trains could travel the distance in 3.5 hours. And travelers quickly noticed that their timepieces were off.
At first each city kept its own time standard, and the traveler would have to readjust the time at their destination. Train schedules soon became increasingly unmaintainable. Over time, this approach soon to be a complete clusterfuck.
Here is where Einstein entered the picture. Today we think of relativity as some abstract concept, but Einstein was thinking through a very pragmatic issue--one that many people were grappling with at the time: Namely what does it mean to say that two events occurred at the same "time"?
He was not just killing time at his day job at the Patent Office. Many of the submissions he was working through were for various technologies meant to synchronize the time between two different locations, often through the use of electromagnetic pulses. But in such cases, what was the "real" time, the time in NYC or the time in Philly? And how to account for the time it took to reconcile the two different times?
His conclusion? No absolute frame of reference exists, one apart from all the other frames of reference.
Apart from light of course. The speed of light stays the same no matter the frame of reference, no matter if you are traveling against it, or in the same direction. All motion is relative motion.
We all sense that we live in the same present. Yet, time moves more slowly for things moving close to the speed of light. This is called relativistic time dilation, and we still don't have the hard-wiring to make sense of it.
Notes taken from the book "About Time" by Adam Frank