Everything started when Brendan Eich wrote a language to run Scheme on the Netscape Navigator. Then, Ryan Dahl got the Google's V8 JavaScript runtime and developers would write JavaScript on the server side.
Nowadays people write JavaScript everywhere (web servers, to fly drones, tablets, mobile phones, refrigerators etc). Isomorphic JavaScript is used to describe JavaScript code that “can be executed on the client and the server”.
React has a powerful ability to render also on the server side. This is huge for perfomance and SEO. Also, sharing the same code between client and server makes maintenance much easier.