I work with HolacracyOne, the company behind Holacracy. We definitely have a lot of work to do to explain Holacracy outside of our trainings & consulting services - we're a young company and haven't focused on that as much so far, but it's definitely something on our radar (especially after this press storm).
To answer your question, the secret sauce of Holacracy is the Holacracy Constitution – it replaces the CEO in deciding how decisions get made and how we organize. See: www.youtube.com/watch?v=31MljhiyxZ8
What is the secret sauce in Holacracy that makes it different from hierarchies?