I think the one-line description of React on its home page (https://facebook.github.io/react) is brilliant:

It's a library for building user interfaces. This is perfect because as it turns out, this is all we want most of the time. I think the best part about this description is everything that it leaves out. It's not a mega framework. It's not a full-stack solution that's going to handle everything from the database to real-time updates over web socket connections. We don't actually want most of these pre-packaged solutions, because in the end, they usually cause more problems than they solve.