I understand BDD to be more about specification than testing. It is linked to Domain Driven Design (don't you love these *DD acronyms?).
It is linked with a certain way to write user stories, including high-level tests. An example by Tom ten Thij:
Story: User logging in
As a user
I want to login with my details
So that I can get access to the site
Scenario: User uses wrong password
Given a username 'jdoe'
And a password 'letmein'
When the user logs in with username and password
Then the login form should be shown again
(In his article, Tom goes on to directly execute this test specification in Ruby.)
The pope of BDD is Dan North. You'll find a great introduction in his Introducing BDD article.
You will find a comparison of BDD and TDD in this video. Also an opinion about BDD as "TDD done right" by Jeremy D. Miller
March 25, 2013 update
The video above has been missing for a while. Here is a recent one by Llewellyn Falco, BDD vs TDD (explained). I find his explanation clear and to the point.