Consider the primary benefit of TDD to be design. It should be called Test Driven Design. BDD is a subset of TDD, call it Behavior Driven Design.
Now consider a popular implementation of TDD - Unit Testing. The Units in Unit Testing are typically one bit of logic that is the smallest unit of work you can make.
When you put those Units together in a functional way to describe the desired Behavior to the machines, you need to understand the Behavior you are describing to the machine. Behavior Driven Design focuses on verifying the implementers' understanding of the Use Cases/Requirements/Whatever and verifies the implementation of each feature. BDD and TDD in general serves the important purpose of informing design and the second purpose of verifying the correctness of the implementation especially when it changes. BDD done right involves biz and dev (and qa), whereas Unit Testing (possibly incorrectly viewed as TDD rather than one type of TDD) is typically done in the dev silo.
I would add that BDD tests serve as living requirements.
