This can be one of the hardest values to understand for some, especially we who live in the third largest country in the would that has one official language ... English. We can drive for three days in one direction, cover thousands of miles, and still speak English to people. There are few places in the world that one language will get you that far. There are many places in the world where you need a couple languages to travel just a few minutes away.
More than a necessity of living, acquiring the language of a place gives you natural access to people. This seems over simple to say, but it is a fact that real access to people and real access to conversations of the heart, real discipleship and influence, happen because of competence in language.
There is also something hard to quantify about learning a language, both in what it does to the learner and in the eyes of the people. There is a road of humility offered to every language learner. The opportunity to not be competent and not be capable for a time, into which (as many of our missionaries have experienced) God moves to mature and prepare their hearts for the work ahead.
There is a shedding of culture and an adoption of culture that happens in the language process. As missionaries, the goal is not to transplant Western culture into another culture, the goal is to transfer the gospel into another culture. Language acquisition and everything that goes with it is one of those tools that help prepare the messenger to be able to speak a purer gospel into another culture.