If someone has the ultimate authority on a topic or decision, you can say they have the last word. Even if your teacher listens to student input on which topics she'll cover, she still has the last word
There are several ways to have the last word. Coming up with the final remark in an argument gives you the last word. Being an expert in a particular in a field can also give you the last word: "She was the director of the state health department, so I consider her the last word on vaccines." And informally, something that's stylish can also be described this way: "Those pink patent leather boots are the last word in spring fashion!"