Okay I'll TRY this as its hard for ME to put into words. React is responsible for the view, period. Instead of coming up with jqueryish ways to handle dom manipulation, React simplifies the process. With the addition of Redux/ Mobx/ Flux, you can also maintain the state of your site / application across all "pages".
I'll give a high level example. Lets say you want to show a div on a button click. Non React we would have to set up some variable (let), in out js query the button, attach an event handler to it, listen for the click, and depending either a) toggle a css class on a hidden div (where we would need query that as well). or b) create a dom element to inject into the space.
Now in a more traditional application, when a user went to a different page and back again , the div MORE than likely wouldn't be there unless you stored the value in session/ local store or sent something to the server to store that flag. But that would mean you would need to make an API call on page load to check for that flag and that's just... dumb.
React:
I set an onClick on my button that sets the app state to "show div: true". I set css classes to read that state for option a or for b it would look like {showDiv && <ComponentIWantToShow />}. Since its an single page application, if I set my state right, navigating back and forth shouldnt be an issue (for something this simple I wouldn't need Redux, I could just use Reacts native context API).
That got a little deeper then I intended.