The first very special thing that was observed about the speed of light is that it is NOT relative. That is, if I fire Alice light beam at you from a moving train, while Bob fires a beam at you from a platform, both beams will reach you at the same time. Sound does not behave the same way, light was the first thing that we observed like this.

This was a gigantic problem, an experiment contradicting one of the most fundamental laws of nature as we knew them at the time - Galileo Galilei's principle of relativity.

Note that this observation has nothing to do with our eyes's ability to perceive light. The same observation will not happen with sound waves; and it will hold even for frequencies of light that we can't directly observe with our bodies, such as radio waves.

As others note, it was later discovered that this is not a special property of light itself. It is in fact a special property of the universe, and it applies to any particle without mass; the photon happens to be the only massless particle that we can directly observe, so it was the one which gave the name to the physical quantity.