Byzantine complexity is anything that is so overly and unnecessarily complex as to be beyond understanding. The implication is often that something with Byzantine complexity is not worth understanding.
History
The Byzantine Empire was the end result of centuries of Roman rule and bureaucratic growth. During this era, a combination of growth of the aristocratic class, the difficulties of administering an increasingly expanding Roman republic led to a complex and opaque system of government that no one who had not grown up inside it had much hope of understanding.
It was so complex that Byzantine complexity has come to refer to any overly complex system.
References
Byzantine complexity Wikipedia(Text) CC BY-SA