React is front-end library. It provides great tooling for creatiing user interfaces. And it creates a single page application. Which means when you open a react app. It does not reload and its really fast.
While you could also use nodejs and something like handlebars to create a website. But that website would be rendered on server and then served to the user. But its alot more than that. There are a lot of things that you want to do on the server. Like authentication. You want that part to be secure. So you keep it on the server.
Now the answer to the final part of your question.
For a fully functional app. You would use react to create user interfaces. And nodejs for creating an API which your react app will call.
