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.