The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second
Why is this so? Who decided that 1/299,792,458 of a second is a suitable measurement? What significance does the number 299,792,458 have? It seems so arbitrary.
This number has no significance. Its origin is historical. Originally the meter was defined as 1/40,000,000 part of the Paris meridian. Based on the measurement of this meridian, they made a standard rod in Paris. Since it is inconvenient to base the definition on something which is difficult to measure, the meter was soon redefined simply as the length of this rod. Then when they decided to use another, more convenient and more accurate standard, defined in terms of light, they just measured the rod and obtained this number.
The reason why 1/40,000,000 was originally chosen is interesting. At the end of 18-century, the French revolutionary government decided to introduce the decimal system everywhere. This included angle and time measurement. So the angle of 90 ordinary degrees became 100 decimal degrees. Therefore, the whole circle had 400 degrees. Each decimal degree was divided into 100 decimal minutes. So kilometer is one decimal minute of the Paris meridian. (Similarly to the nautical mile which is one ordinary minute of a meridian). According to the project, also nychthemeron (day+night) were divided into 20 decimal hours, and decimal hours into 100 decimal time-minutes.
Unlike other decimal units, these did not survive, and were abolished by Napoleon. One can still find on e-bay French decimal watches and angle measuring instruments made at that epoch. Unlike decimal hours, decimal degrees are still in use; they are called grads.
It's no more arbitrary than any other measurement unit, including the second. Nearly all modern values were chosed to try to avoid changing existing units' values while providing a source less subject to variation.
The most well-known example is the kilogram. There's a standard cylinder platinum&iridium of which served as the original kilogram for quite a while. But even that is subject to evaporation as well as impurities. There were/are plans to carve a perfect crystalline silicon sphere, which would be less subject to those problems. However, as mentioned in Wikipedia,
2019: The kilogram is redefined in terms of the Planck constant.
So ultimately all ISO / NIST units now refer back to fundamental constants. We can only hope these are as (literally) universal as we believe they are.
There's an important point that seems to have been missed here: it was initially proposed that the metre would be the length of a pendulum whose period would be equal to one second, when let swing at the surface of Earth.
Unfortunately, it was realised only too late that in fact because acceleration due to gravity varies slightly depending on where you stand on the surface of Earth that of course a pendulum that has a swing period of 1 second in one place will have a different swing period in another.
However, it was noticed that this length was close enough to the 1/10,000,000 the distance from the North Pole to the Equator through Paris, that the latter was what was ultimately chosen.
It is only so much more recently that the exact length is now established by defining it in terms of the speed of light, about which I don't need to comment because someone has already said it.
But if you've ever wondered at the coincidence that acceleration due to gravity at Earth's surface measured in metres per second squared is interestingly close to pi squared --- that's why.
