This is really awesome. One of my good friends is a linguist, and when I first started learning about languages, I couldn't figure out what all the hype was about. Yeah languages are dying... So what? A single language where I could communicate with anyone in the world would be the best, wouldn't it?
A language is like a toolbox for idea transmission, we want to share what we see on the inside, and language is one of our best ways to do it. It's the most universal, it's one of the first things we learn, and it has the ability to incite the most powerful imagery (books vs. a movie).
Say a language is the average mean of a group of people's ability to speak to one another. These people were likely geographically isolated and their language developed on it's own, they saw things in the world and described them with their language. Their culture, their ideas, their perceptions of the world are all encoded into their language. When all the native speakers of a language die, we lose more than just the language, we lose the insights that the language carried, a language that was likely crafted over many thousands of years.
Take for instance color blindness. Attempt to explain to someone with color blindness what colors look like. It will never work, they will never experience what you experience, but they can share your experience through your description of colors, they can imagine what the world could be like if you give a good enough description. We lose analogies for human thoughts when languages die, and if we ever want to begin to understand what a consciousness is, preserving these analogies is an absolute necessity. We could wonder for millions of years whether or not a language could ever come to be that didn't have counting words, but luckily we found the Piranha[1] that do just that [2]. It's like all the species we're losing in the rain forests, what if the cure for cancer was present in one of the now-extinct mushrooms? What if we never could find the cure for cancer because we just didn't have that mushroom? It likely won't happen for cancer, but for consciousness we need every piece of information that we can get.
[1] http://www.newyorker.com/reporting/2007/04/16/070416fa_fact_...