ember-rails is a Ruby gem that is actually used in Discourse.
Discourse staffers are far better to comment, but broadly, EmberJS deals with the front-end, and Ruby-on-Rails, the back end. Of course, Discourse has elements of a bespoke architecture and the exact configuration is, like any big application, at least somewhat unique.
A nice description of the way things work is here Creating Routes in Discourse and Showing Data
The API docs are here https://docs.discourse.org