Justinian the Great was a Roman/Byzantine Emperor from 527 to 565, one of the most famous Roman Emperors and probably the most well-known Eastern Roman Emperor. His well-earned reputation is due to his eventful life, richly described in Procopius' accounts, and his famous portrait mosaic in the Basilica of San Vitale, Ravenna.
His rule was marked my many momentous events, like the Nika riots, the making of the Corpus Juris Civilis (the basis for Civil Law applied in continental Europe and beyond), the reconquest of North Africa (meaning modern Tunisia, eastern Algeria and western Libya aka Tripolitania), the Gothic wars that devastated Italy, the seeding of the Lombardic control of that same peninsula, the Battle of Dara, the Sack of Antioch in 540 and, perhaps more important, but completely beyond his control, the Justinianic Plague, the first pandemic of Yersinia pestis.
As huge Byzaboo/Byzantophile, I'm glad he's been chosen to represent this sub, but I have to ask why, among all the other historical figures, has he been chosen?
Back in the distant past, known as 2012, it was decided that we needed a custom Snoo, so a call went out to the community. Several users answered the call, but it was agreed that /u/Ambarenya's creation of Snoostinian was the coolest. A year later, the design was revised slightly by /u/sukritact into a more detailed vector image.
So there wasn't really any specific impetus behind the choice, it just... happened. We now have quite a large collection of additional Snoos, but he remains our Jerry West..