Vernacular describes everyday language, including slang, that's used by the people. The vernacular is different from literary or official language: it's the way people really talk with each other, like how families talk at home.
You know how some language is fancy and formal? Vernacular is different: think of it as how friends talk when no one is listening. Vernacular language includes slang and obscenities. One of the hardest things about writing for school is getting away from the vernacular and learning to write in more formal ways that don't come as naturally. You can also say specific groups have a vernacular, meaning the unique way people in a certain region or profession speak.