The title is not really accurate. Language obviously has something to do with words. Language, generally speaking, is made of words. But the importance of words to language is, I think, a little overrated. Hmm, that's not really right either. Words are, after all, essential to language. No words, no language. No words, no blog post. Hard to be overrated when you're essential.
So let's try it this way: vocabulary is not the most important part of learning a language. We might add a corollary to the same effect about grammar. And yet, vocabulary and grammar rules make up the core of how we teach and learn language, whether foreign or our own. To me, this is like trying to teach someone to play piano by making them memorize the names of the notes (something many music educators do, of course). It's not useless, it's just not the most important part.
So what's the alternative? Well, I think there's a strong argument to be made for the importance of culture in learning. Can you truly learn to speak a language without an appreciation for how and when and where it is spoken? Perhaps you can, in a mechanical kind of way, but there's a reason why people learn more about how to speak Spanish by living in Spain for a few weeks than by taking years of courses.*
* This was certainly my experience, though you have to exchange Spain for Costa Rica.
Language is a cultural phenomenon. Think about how much of what you say is idiom, context, suggestion, gesture. Even in written text, there are cultural meanings and expectations. We learn to read not just words, but the meanings of words. We learn to listen not just to grammar, but to intonation and inflection.
Of course, none of this is a revelation. The importance of cultural context to language may have been news long ago in anthropological and even educational circles. As early as Wittgenstein, modern philosophy began a deconstruction of our concept of language which has meaning outside of context. No, the point isn't that this is news.
Rather, this is a gentle reminder - to myself, or to any educator - that language has everything to do with culture, and nothing to do with words.