GraphQL is a communication protocol that allows web applications to communicate. It is similar to the much hyped REST APIs, but is more uniform and thus more universal. This makes GraphQL usable across CMS products.
Calypso is heavily built on technologies that come from the world of Facebook, especially the combination of React.js UI library and the Redux Flux architecture implementation.
GraphQL is also a Facebook initiative, so one would think it’s a drop-in-replacement for the WordPress REST API. But currently as of June 2016 the effort is in so much work that there are no visible signs of WordPress Calypso for taking GraphQL into use.
Instead WordPress continues to utilise it’s own communications library, WPCOM, that uses a custom version of the REST API that is currently only available to users of the proprietary hosted WordPress.com content platform similar to Medium.
In the future WordPress may well choose to go with GraphQL, but it using Facebook technologies does not guarantee this as the communication layer is separate from the UI. In addition it’s worth noting that the WordPress REST API itself is not progressing as smoothly as it could.