The WordPress REST API is a relatively new addition to the WordPress platform. Before it was added to core, the REST API was available as a standalone mechanism via a separate plugin. You could get everything and also learn how to work with the package from the project's official website at http://v2.wp-api.org/.
However, starting from WordPress 4.7, REST API is now included in the core WordPress package, and you don't need any additional plugins or tools to make it work. Basically, as long as you're on the most recent version of WordPress, you have REST API installed and enabled by default. Which is great news! But let's get a bit deeper.