Vagrant manages virtual machines. Docker uses linux containers, which is essentially "chroot on steroids" [1]. A linux container is just an isolated process (from which you run your code) on the host machine, like a FreeBSD jail. The host machine can peer into the container, but the container cannot see the host machine. Docker just helps to automate and manages the linux container life-cycle.

p.s. I'm planning on doing a couple screencast episodes about linux containers and docker on my website, which should be online in the next week or so @ http://sysadmincasts.com/

[1] http://lxc.sourceforge.net/