I think the one-line description of React on its home page (https://facebook.github.io/react) is concise and accurate:
"A JavaScript library for building user interfaces."
It's a library for building user interfaces (UIs). 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 WebSocket connections. We might not actually want most of these prepackaged solutions.
If React isn't a framework, then what is it exactly?