The RTM API allows integrations to connect to slack from behind a firewall, seemingly connecting much like a normal desktop client might, from any computer, not just an externally visible server.

It's a very important enterprise feature for those wanting to integrate Mattermost with their internal applications.

Further discussion on this can be found here:
https://forum.mattermost.org/t/does-mattermost-support-real-time-messaging-api-from-slack/1287/2

And this slack FAQ describes the differences between the Events and RTM API's:
https://api.slack.com/faq#events_api

This is the Slack RTM API spec:
https://api.slack.com/rtm