Byzantine complexity is a phrase used to refer to anything overly and unnecessarily complex; so complex as to be completely beyond understanding. (There is a connotation that it is not worth understanding.)
History
The Byzantine empire was the end result of centuries of Roman rule and bureaucratic growth. The end result of the combination of aristocracy, the remnants of the Roman republic, and time was a complex and opaque system of government that no one who had not grown up inside it had more than a hope of understanding. (And many inside felt they had no hope of understanding.) In fact, it was so complex that its very complexity became a watchword in surrounding areas and in governments that had to deal with it that the term 'Byzantine complexity' became a general term that was and is used to describe any overly complex system.
See Also
