I'm very confused as to what this is and how you'd go about "building user interfaces" using this. Is it an Ember/Angular competitor? Does it replace or complement a back-end stack?
React is not a standard MVC framework -- we simply strive to be a fast and easy-to-use way to build UI components. You can integrate with any backend (or frontend!) stack that you want.
The reason you'd probably want to use React is that there aren't a lot of concepts to learn, it's fast out of the box, and it ensures that your UI stays consistent with your data without manually specifying data bindings or anything like that.