Docker uses LXC containers. In Linux, these aren't VMs and are light weight user-land separations that use things like cgroups and lots of really special kernel modules for security.
Unfortunately, this means Docker only runs on Linux .. not even Linux...special Docker Kernel Linux (all the features they need are in the stock Kernel tree, but it's still a lot of modules). In Windows/Mac, you still need to run in a virtual machine.
Even with this update...you still need to run in a virtual machine. It's not actually running Docker natively. It can't, even on Mac which has a (not really) *NIX-sh base. You have to then use the docker0 network interface to connect to all your docker containers.
In Linux, you can just go to localhost. I _think_ FreeBSD has native Docker support with some custom kernel modules. I'm not sure...I've only looked at the Readme. I haven't tried it.
So even in Windows/Mac, all your containers do run in one VM (where as with traditional stuff you mentioned, you'd need a VM for each thing). Docker containers are meant to handle one application (that it runs as root within its container as the init process ... cause wtf?). With VMs, you'd typically want some type of configuration management (Puppet, Ansible, Chef, etc.) that sets up apps on each VM/server. With Docker, each app should be its own container and you link the containers together using things like Docker compose or running them on CoreOS or Mesos.
In my work with Docker, I'm not sure how I feel. LXC containers have had a lot of security issues. Right now, Docker doesn't have any blaring security holes and LXC has increased security quite a bit. CoreOS is pretty neat and I wouldn't use docker in production without it or another container manager (the docker command by itself still cannot prune unused images. After a while you get a shit ton of images that just waste space you're not using. CoreOS prunes these at regular intervals. A docker command to do this is still a Github issue. Writing one yourself with docker-py is horribly difficult because of image dependencies).
Oh and images. Docker uses images to build things up like building blocks. That's a whole thing I don't want to go into, but look it up. It's actually kind of interesting and allows for base image updates to fix security issues (although you still need to rebuild your containers against the new images ... I think...I haven't looked into that yet).
Docker is ... interesting. I find it lazy in some ways. I think it's better to build packages (rpms, debs). FPM makes this really easy now. Combine packages with a configuration management solution (haha..yea they all suck. Puppet, Ansible, CFEngine...they're different levels of horrible. Ansible so far has pissed me off the least) and you can have a pretty solid deployment system. In this sense, Docker does kinda make more sense than handling packages. You throw your containers on CoreOS/Mesos and use Consul for environment variables and you can have a pretty smooth system.
I dunno. I'm trying to actually like Docker. I've only made fun of it in the past, but now I work for a shop that uses it in production. O_o
:-P