So, when you ran the Docker Quickstart Terminal application, it created a bunch of certificates, SSH keys, and configured your user's environment to run Docker. It also launched a virtual machine running Docker.
This will list the names of any active machines, the default machine launched when you first install Docker is called
default, if you run:
docker-machine status default
It should tell you that the virtual machine is currently running. Finally, you should be able to SSH into the virtual machine by running the following command:
docker-machine ssh default
You will notice that when you SSH into the virtual machine, it is running the Boot2Docker distribution.