Beyond any other definition, Behavior Driven Development/Design ("BDD") is a philosophy.
"BDD" is a set of tools and techniques that exist to support one idea: good software is written to meet the needs of the stakeholders (typically clients).
These stakeholders know their business better than the people designing the software. It is the responsibility of developers to capture the business requirements and translate them into software.
BDD tools facilitate this as a process by letting developers author features first, which capture requirements in a domain-specific language. Code is developed by working on these high-level features, and then on code specifications.