Originally, the time of day was tied directly to the sun. The highest point of the sun was 12 noon, so each place that was on a different longitude had a different time of day.
For example, shortly after 1780 there was an early 'time service' in Dresden. In the observatory of the Physikalisches Kabinett in the Zwinger, the highest level of the sun was determined through a passage telescope. Then the exact time was passed on to the surrounding town halls and churches by a mounted messenger with the help of a pocket watch.
Image source: https://berufe-dieser-welt.de/postreiter/
Since the sun seems to move slowly and sometimes faster across the sky, a steady clock does not correspond to this local time. Since the time of day had to be corrected anyway with the accuracy of the clocks of that time, this initially played no role.
Only when you got faster by traveling by rail did you have to find a solution. Initially, every train had to have the time that corresponded to the original departure point. As the railway lines increasingly crossed, something had to be done about the confusion of times.
The following film excerpt is from "The Stuff the Cosmos is Made of - DVD 1 - The Illusion of Time" (2011) by Brian Greene. Published at daylimotion:
While the railways initially used the local time of the main towns (Prussia and Alsace-Lorraine - Berlin, Bavaria - Munich, Hesse - Frankfurt), it was decided in 1891 to use the mean local time of the 15th longitude as the mean railway time. This corresponds to today's Central European Time (CET), which was legally established on April 1, 1893 for the entire German Empire.
This means that the sun is at its zenith at 12 p.m. CET in Görlitz on the German-Polish border, and at the site of the Saarland watch museum only at 12:33 p.m.
However, there are deviations - see next page:
Equation of time 1
The earth revolves around itself.
We see this as an apparent movement of all heavenly bodies from east to west.
The earth moves around the sun once a year.
For us, this shows up as the sun's apparent lagging behind the fixed star sky as the background. Due to this apparent lagging behind, it itself completes an entire orbit along the fixed star sky within a year on the same path of the sun (ecliptic).
The earth's axis is inclined to the earth's orbit axis by 23.5 °.
This shows up for us as an inclination of the sun's path by this angle (inclination of the ecliptic). As a result, the sun is 23.5 ° higher on June 21 and 23.5 ° lower on December 21 than at the same time on March 20 or September 23. This is how the seasons arise for us.
Equation of time 2
The earth does not move on a circular orbit with constant speed, but on an elliptical orbit with non-uniform speed around the sun.
For us, this is shown by the fact that the sun moves sometimes faster and sometimes more slowly. In the course of exactly one year, these fluctuations are evened out again. On the days in between, however, the true sun runs either ahead of or behind an imaginary sun that would travel at a constant average speed.
Graphics: CC license Wikipedia
If you determine the position of the sun at the same time every day, the equation of time shows that the sun seems to lag behind or run ahead of the earth. There are four days when local time at longitude 15°E coincides with CET.
Example: The photo was taken at around the 8th degree of longitude and 50th degree of latitude in Germany. If the position of the sun (white dots) is determined every 7 days at 9 a.m., the result is an apparent path of the sun, the analemma.
Photo montage: CC license Wikipedia