Courtesy of Jetpack bundle from WordPress, JSON API allows applications to securely access your content thru the cloud. For example, if you want to make a custom iOS application to pull your blog posts (not referring to RSS feed here) you will need API. Also as a live example, installing WordPress for Windows 8 and configuring your WordPress blog or website will require you to activate JSON API. So, should you decide to pull your blog posts to the 3rd party apps, Jetpack JSON API should be activated.
Jetpack will allow you to authorize applications and services to securely connect to your blog and allow them to use your content in new ways and offer you new functionality.
Developers can use WordPress.com’s OAuth2 authentication system and WordPress.com REST API to manage and access your site’s content.