From what I understand the overhead in performance is negligible, while giving you very fine grained control over your resources. Say you have a web application, a front-end reverse proxy, a database, a cache, a background worker process, and a message queue. Throw all these components into separate containers on a single server while the load is low. Then move the DB container into a separate VPS as your traffic grows. Or try doing an upgrade of the message queue in a brand new container, and if it fails, just don't use it.
Sure, you can do the same thing with a VPS, but then you are paying the per-hour fee for it, while 99.99% of its resources will go unused.
I think what we're saying is that in addition to using awesome IaaS services, you can use Docker to solve any number of issues like utilization, deployment, etc., whether they be with your existing providers, on bare metal, or on OpenStack (which can do both.)
I personally have a Linode VPS where I continuously run about 30-40 containers powering the various services/demos I create. I'm looking forward to migrating to the new offering.
You're already running VMs with 1-service per-VM for the sanity of dev-ops, right?
Instead of 1 VM per-service, with docker, you can make 1 larger host, run 1-service per-docker container, and get more performance out of a single machine.