In a typical jQuery/Backbone kind of app, you've got some data in something like Backbone models and you've got state stored in the DOM. Keeping those two in sync bring complexity in. The React model is
simpler (in the non-intertwined sense... see Simple Made Easy[1]) in that you have data in one place, a function that transforms the data to UI and the browser DOM is managed automatically from that.
It's not perfect but it reduces complexity.
[1]: http://www.infoq.com/presentations/Simple-Made-Easy