My university library opens in about twenty minutes, where I'll have access to a The Cambridge history of western textiles. I've never read it, but I think highly of the Cambridge University Press. I might as well throw this out there though:

What does that even mean?

For any pre-industrial state, the foundation of their economy was almost always agriculture. You could say that it provided a healthy tax base for the Byzantine government, which is common (the Han dynasty was heavily reliant on its monopoly of salt and iron). Did it provide a unit of account? Did it employ a large number of people? Was it similar to the slave trade for many North American colonies, in that plantations relied heavily upon slaves? Unfortunately the article is so vague about that, that the only way we will know is to read the source. Which I do not have unfortunately.

Just food for thought.

EDIT: Cambridge University Press does not disappoint. This is all based upon information in chapter 6 of The Cambridge history of western textiles, which was written by Anna Muthesius, Professor of Textile Studies at the Surrey Institute of Art and Design and an Honorary Member of Lucy Cavendish College, University of Cambridge.

The short answer? That claim is, indeed, correct. The long answer? Read on!

Silk was in fact not only important in the Byzantine Empire, but in the entire Mediterranean, both for Christians and Muslims. Here are some key points.

• It did indeed operate as a form of currency. It was highly liquid, meaning that you could be anywhere in the Mediterranean and could instantly trade it in for cash (or, err, gold). Further, it was valued so highly, that military aristocracy would hoard it like gold in times of emergency. Silk was worth its weight in gold. There are two large reasons for this. First, silk was accepted anywhere in the Mediterranean. Second, silk was never discarded. Part of this is because of its high value, but also because silk is very easy to reuse. Silk was almost never thrown away, and silk that was gifted by the Emperor could easily end up in a monastery.

• It had a very important political and diplomatic function. Silk operated almost like an international currency. Not only did people accept it everywhere, but governments took it as well. Much of the relations between Byzantine and the Franks was facilitated with silk. Much of the far-flung Byzantine territories were aided by or defended by Italian city-states like Venice, who were paid in silk or given silk trade rights in the Byzantine Empire. It had a very powerful political and diplomatic value, both within and without the Byzantine Empire.

• The production of silk was a very prestigious position. Muthesius provides one example, by a man named Michael. He was one of the directors of an area called Zeuxippos, an imperial factory for silk (there were both imperial and private silk guilds, but the imperial guilds held various monopolies on different kinds of silk from the fourth century to the thirteenth century). Michael was one of the directors of this guild, but he was also the director of the eidikon (a special treasury and storehouse, mostly for silk) and he was a master of the imperial bedchamber.

• The Byzantines were trend setters in silk. The Franks adopted many of the Byzantine rituals surrounding silk, and eventually Islamic and Byzantine silks would be nearly identical in style. The Islamic world even copied court furnishing styles and dress codes that the Byzantines used. Silk was made in the Islamic world, but the Byzantines were the dominant silk producers during this time in the Mediterranean.

• The Byzantine silk industry was losing importance largely to foreign competition. By 1000A.D. raw silk was made throughout the Mediterranean. The biggest source of competition was Italy. King Roger of Sicily had captured Byzantine and Islamic silk workers and started his own silk industry. Silk production would slowly move up the Italian peninsula, where city-states such as Lucca and Venice would start producing their own silk. Another reason, however, was the Fall of Constantinople in 1204, which was the center of the Byzantine silk industry, but demand was not haltered at all by this event.

• Finally, raw silk was made throughout the Mediterranean; however, to finally emphasis the importance of silk, it was illegal to sell raw silk in Constantinople. The domestic silk industry was so large, that the entire domestic raw silk production was used for the weaving industry. In fact, the Byzantines imported raw silk from Syria and Egypt to be woven in Constantinople.

EDIT: I changed Anna Muthesius's bio. She does have a website, but I trust the book's bio on her more (if only because there might be two with the same name). It also mentions two books she wrote: Byzantine Silk Weaving (1997) and Studies in Byzantine and Islamic Silk Weaving (1995)

No, the silk trade was not really the foundation of the Byzantine economy. The reason the Byzantine economy was so vibrant during the collapse of the Western Roman Empire was its access to trade routes, most notably the Silk Road that led into India and China. As its name suggests (its name is derived from ornate silks that were traded along the route long before it opened to European access) the silk trade was indeed a part of what comprised the trade route.

A few monks stole silkworms for the emperor, and this gave Byzantine a monopoly on European silk production, but silk was not at all the most important part. What was really important was that the Byzantine Empire had a very strategic trading port located at Constantinople, and was the western end of the Silk Road. It impressed travellers with its fabulous display of wealth in the capital, and was very active in maritime trade.

It's very rare that an empire's economy be based around one form of production. Much more commonly, geographical location and ability to interconnect with other nation-states through trade (and conquest) were much more foundational in a nation's economy.

I wouldn't say that there was any really particular commonity that powered the Byzantine economy. In fact I don't think its really the trade goods at all but more of trade routes itself that powered their economy.

The Byzantine empire really is the gateway between east and west. The Silk Road essentially has to pass through it in order for there to be trade between Europe and Asia. So really its actually the tariffs and taxes placed on trade goods that helped fueled the economy. The ottomans that replaced them later on replicated this economic policy as well.

They can basically place a price tag of what ever value they want on a commodity.

Edit: TD;DR the Byzantines weren't really a that much of a trading state but more of a toll booth for trade.