In the documentary movie "$E=mc^2$ Einstein's Big Idea?", the narrator says "Einstein had a monumental insight", when Einstein and his close friend were looking at the clock towers in the city. Einstein seems to be so excited here and thanks to his friend to go home and work as I guess but I am very curious what is so exciting here but I can't get what exactly is triggered in Einstein's mind here which is implied by the narrator. Einstein says "I've completely solved the problem." What is the implication here? What is its relation to clocks at different distances? Is it possible for you to describe it to a person who is not a physicist but knows basic undergraduate physics?
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I'd say it's all about time is flexible and not absolute as until then was thought, being the speed of light the one that remains the same. He would see that clock tower every day on his way to the patent office and suddenly realize (maybe as said in the movie) that if he were traveling at near the speed of light, the clock on the tower would slow down or eventually to stop at $c$ speed; meaning that time is relative to ones motion. Conclusion: the faster the travel, the more time slows for the traveler.