It is built on top of docker and Kubernetes (CoreOS/fleet in v1), and lets you deploy docker containers natively and/or automatically builds those for you using Heroku buildpacks or Dockerfiles when doing git push deployments. You can also drop down to the Kubernetes level if you need to for things that don't really fit the 12-factor app model without breaking Deis.
That being said, I'm totally biased as I wrote an Heroku-like UI for it (http://deisdash.com/about) and using it for our infrastructure at work. Other similar alternatives are http://pivotal.io/platform, https://flynn.io/, https://www.openshift.com/, https://github.com/dokku/dokku (for single server), etc.