In lieu of a better term, behavior-driven system administration is the application of BDD principles to system administration, primarily building and maintaining systems.
The RSpec Book by David Chelimsky et al presents BDD as using the tools Cucumber and RSpec. Cucumber is used to describe and test the feature to be implemented and then RSpec is used to test the implementation while it is being built.
In Test-Driven Infrastructure with Chef, Stephen Nelson-Smith states that RSpec is not used in his example in the book because "there's no point in unit testing a declarative system." On one hand, I can agree with the statement. Somewhere, I read software developers saying that you should test your application but not worry about testing the platform.1
On the other hand, I disagree. I think RSpec can be useful when testing a declarative system but my rationale has less to do with testing than with auditing.2 I see Cucumber and RSpec tests as filling two different roles: Cucumber verifies the system's behavior. RSpec verifies the system's state.3 This also lets me use the Cucumber features to document the system's behavior and RSpec scenarios to document the system's state. (As pointed out in one of the BoF sessions at LISA 2011, Puppet manifests don't themselves work as documentation of a system.)
I am currently working on building a new system where I hope to test this. I have RSpec scripts written for making sure Puppet is set up and correctly configured but I haven't completed the Cucumber feature for Puppet to verify it's behavior so I can't show how this works in practice. When I have a full example, including a working Cucumber feature and Puppet config, I'll make another post and walk through it. (Or if it doesn't work out, I'll point that out too.)