This was the question I was asking myself a while ago, when I wanted to start learning React. I was quite surprised about how difficult it was to find a simple answer to this. As I now feel I am somewhat onboard with the topic, I feel confident to write about this and hopefully give some guidance to people facing a similar issue.
Being just a library, React only serves for the purpose of the view, which essentially means that React is just meant for building the interface of your application. Because it is just meant for the view, you cannot really compare it to Angular or Ember, which are actual frameworks, since they provide more than just the view.
React, being just the view, makes getting started with it actually more confusing, because you really cannot build a fully working application with React only. There is now a lot of other stuff that you need to get a grasp on as well, to be able to complete the whole ecosystem. If you're totally new to the topic, my recommendation is to just skip this part for now since, for starters, it might be a bit overwhelming. Let me rephrase that: it IS going to be overhelming.
You have now gotten a brief introduction to React, but we have not really covered why you should use it. The benefit of React is the virtual DOM. The normal HTML DOM like, for example
<p id="html-dom">HTML DOM</p> does not really do much by itself. The virtual DOM on the other can. It can "React" since, when something changes, the UI re-renders.
But now it is time to get your hands dirty. Check out this great introduction video to React from Dev Coffeee.