Well Docker I believe is a fork of LXC (some people state LXC is a derivation of OpenVZ for the main kernel), or much simply it's just LXC with more features. I believe within it's design parameter it's focused on more application deployment, scalability, and user friendliness.
When I say application deployment I mean very similar to OpenVZ Templates (or those turnkey solutions) but executed in what several other people claim "a much better and easier fashion". This also brings in Scalability because... come on... you can setup more deployments of your software whenever needed, and by user friendliness they mean easy to setup (without needing a different kernel) and tools to help someone manage it much easier. Obviously OpenVZ and Docker really share similar "features", but I believe Docker was built with the focus on these features.
From the LET discussion, someone linked to the IBM Research paper focused on the performance difference between each virtualization technology:
http://domino.research.ibm.com/library/cyberdig.nsf/papers/0929052195DD819C85257D2300681E7B/$File/rc25482.pdf
Also refer to this stackexchange that talks about the difference between LXC and Docker:
http://stackoverflow.com/questions/17989306/what-does-docker-add-to-just-plain-lxc
So my opinion is I think it's be really cool to use and I should definitely look into it. Unfortunately, others state Docker is mostly designed for self-use (as in not really secure enough for "selling"). Now I haven't seen actual proof of this (mostly because I spent about 10 minutes to research all this above), but better safe than sorry. Sometime in the future, I'd like to use Docker.
So... tldr: Docker is like the third generation spawn of software virtualization that focuses on deployment, scalability, and user friendliness. I think I'd like Docker.