Ummmmm, big, big question.

As Itsalrightwithme posted, Amalfi was the first major trading-node in post-Roman Italy. That said, it declined WELL BEFORE the 1300's. While it survived as a major port into the 12th century during the Norman period, the fact that it was no longer ruled by the Roman Empire from Constantinople robbed it of some of its importance as a vital connection to the eastern Mediterranean.

Venice, on the other hand, always maintained close ties with the Roman Empire. After the various settlements that were clustered around the lagoon of Venice coalesced into a unified settlement around the Rialto after the Carolingian invasions the Venetians underlined their connection to Constantinople and sent a yearly diplomatic mission to the city securing their right to self rule until Venice helped to sack the city in 1211.

In addition to securing valuable connections to one of the most important polities in the eastern Mediterranean, Venice's convoy tactics helped to develop their economy as early as the 9th century. Initially, the Italian city traded in salt (a commodity that remained a money spinner until Napoleon dissolved the oligarchic republic), probably slaves, and amber.

The full story is, of course, far more complicated than that. I could answer any followup questions regarding the developments of the later Middle Ages and the emergence of Venice's great rival, Genoa, about 50-100 years after that of La Serenissima.

A reply to /u/StoneRose5

To quote the estimable Fernand Braudel speaking of the 8th and 9th centuries: "Along the coasts of Italy, seaports began to thrive -- not only Venice, which was still insignificant at this time, but ten or twenty little Venices." The richest of them was Amalfi, who may have continued to thrive except for a series of invasions by the Normans and Pisans. After Amalfi's decline in the 1300s, three trading cities rose: Venice, Genoa, and Pisa. They conducted trade between the three major "powers" of the time: Latin Christians, Byzantines, and Muslims. Venice, by virtue of her location, was able to take advantage of the Byzantine's sedentary state at this time, providing critical services to them in areas of trade, transportation, finance. In particular, the disastrous Fourth Crusade crippled the Byzantine Empire and Venetian merchants were able to gain very strong concessions from Byzantine emperors and merchants alike.

What about Genoa and Pisa? Genoa had the early military advantage against Venice, although the end of the 1300s brought advantage to Venice. Regardless, in this era the balance of trade shifted further to the eastern part of the Mediterranean, to the advantage of Venice against Genoa and Pisa; further, Venice held key to the Adriatic sea and to a large extent the eastern Mediterranean. She had colonies in Zara, Crete, Dalmatia, Cyprus.

As the Ottomans rose to power and defeated the remnant of the Byzantine Empire, Venice continued to take advantage of her resources to negotiate, cajole, bribe her way into the trade through the Ottoman empire and the Mamluks. This privileged position allowed her to be extremely wealthy when other Christian European entities could not directly access the Silk Road trade.

Of course, nothing lasts forever. Portuguese discovery of a sea route to the East Indies shifted the pattern of trade from Venice at its center to the Low Countries at its center: the rich German banking family the Fuggers were theoretically based in Augsburg but used Bruge and Antwerp as their entry points, and soon the Portuguese started to sell their spices through warehouses in the Low Countries directly. Further, enmity between Venice and the Ottomans meant open confrontation, complicating their trade in Eastern Mediterranean.