http://www.openmindedinnovations.com/blogs/3-ways-to-integra... is a decent, although old article on the three different ways that it can be done.
I personally recommend https://github.com/shakacode/react_on_rails as the solution to this issue. Instead of merely providing you with React and React only like https://github.com/reactjs/react-rails does, it welds Node & Rails together to enable you to use the latest and greatest of the javascript ecosystem.
As for the benefits of doing so, having started my web development journey with Rails, I like to think that Rails provides an excellent convention for Backend MVC & ORM while Node gives you access to up-to-date javascript libraries & frameworks. Combining Node & Rails allows to you to exploit the strengths of both systems in exchange for dealing with greater complexity.