Byzantine does not only say that something is hard. It says the difficulty comes in layers: a rule, an exception to the rule, and an exception to the exception. Each step needs another form, another office, another signature, and very few people ever see the whole thing. Because of that it usually sits next to words like system, rules, process, bureaucracy and complexity. It carries a tired, slightly annoyed tone, as if the speaker has been through it. In this figurative use the word is often written with a small b.

This is the plain historical use. Byzantium was the city that became Constantinople and is now Istanbul, and the empire ruled from it lasted from the fourth century until 1453. The word covers anything belonging to that world: Byzantine emperors, Byzantine coins, Byzantine art with its gold pictures, and Byzantine architecture with its round arches and great domes. It also names the Byzantine Rite, a way of holding church services that Eastern Orthodox and some Catholic churches still use today. In this use the capital B is normal, because the word comes from a place name.