Every time you speak, you are entertaining an audience, whether you are talking to one person or a group of people. If you want to get your message across, you need to keep your audience interested and engaged; a large vocabulary can help you do this by varying your word choices. If you use a few synonyms to describe the same thing multiple times, your speech will be more interesting and people will pay more attention to you.
A large vocabulary helps you express yourself more precisely. The English language, like all languages, is nuanced. "Big" has a broad meaning; "massive" and "enlarged" have different meanings, because the former refers to something extremely large and the latter simply means larger than average. A large vocabulary lets you describe things to a finer level of detail, thus making your point clearer.
The world cannot be described adequately at a sixth-grade level. To really understand what is going on in the world you need to read slightly higher-level publications than a newspaper. A large vocabulary will help you better understand higher-level publications and therefore better understand the world.
You may be smart, but without a large vocabulary people won't know that you are smart. A large vocabulary is associated with intelligence, which means that people will take you more seriously, both at work and in your private life. Regularly putting your large vocabulary to work will improve people's estimation of you and lead to more social success.