Language isn't just a way of sending messages between people. Certainly that's the easiest of its functions to pinpoint, but it does some other really important things, too.
Have you ever asked yourself whether you think in words? I know I do. I've always assumed it's possible to have internal thoughts without words involved, but it doesn't happen that way much with me.
Lev Vygotsky, a famous researcher who was born in Tsarist Russia, had a really interesting idea (actually, lots of them). He posited that language is interpersonal first, and internalized second. Thus, that children will learn the interpersonal function of language with caregivers and others first, then learn to talk to themselves out loud, and finally learn to speak to themselves internally. One thing he observed from child behavior was that whenever children were struggling to accomplish something just at the limits of their capability, they would start talking about it out loud. How to get an object off a high shelf, for example. His idea was that using language actually helped them to grasp what to do next.
This isn't just true for kids. It's true for me, even now! When I'm working on something hard, I talk to myself, or to others (my long-suffering critique buddies will attest to this :-) ).
Language helps make it happen.
Another thing that language makes happen is social interaction. A lot of the language we use is geared less to message-sending per se than to social smoothing and posturing. Europeans in the United States would probably draw attention to our tendency to say "have a nice day" a lot. Some might say excessively, though I've always rather enjoyed hearing it, myself. Then there's "how are you?" "fine" when neither person really has the time to talk about how they're really doing. These are things we use to say "I acknowledge you" and "we're socially aligned."
Greetings can be very important. How they're done can make the difference between feeling that a person is standoffish or friendly, and this can influence all subsequent interaction. So if you're working with a world that has status distinctions, I encourage you to consider building these distinctions into the greeting system. There are also words that we use to mitigate problems, like trying to share a path (excuse me), or remedy a mistake (sorry, pardon me, excuse me).
Often, words are used to indicate the beginning or end of an activity (including, but not limited to, a conversation). In English we'll often indicate that we're changing topics by saying "okay." I also find myself teaching my kids to say "welcome" and "come in" when our friends arrive for a visit, and "goodbye" and "thank you for coming" when they leave. Of course, when we leave their house it's "thank you for having us." In Japan when you invite someone in you say "go ahead, please come up." This, for all you worldbuilders out there, is a great way to give extra information about culture and architecture. The saying "please come up" depends on the fact that Japanese people take their shoes off in a lower entry area called a genkan and then take a literal step up into the house. Many of us know that when we enter a Japanese restaurant we hear the word "irasshaimase"; this one means "honorably come (in)". Japanese also has words you use when you start eating (itadakimasu, I humbly receive) and finish your meal (gochisoosama, it was a treat/feast).
As you're writing language use into your stories, think about how characters can use language to make things happen and to make things smooth. This will not only make interactions feel real, but give you extra opportunities to slant the content subtly and divulge more about the physical and social structure of your worlds.