Okay, there are a few things going on here.

First, the Black Sea region itself. It was a huge producer of grain. Both Genoa and Venice sought to intervene as middlemen, selling the Thrace/Black Sea grain to Constantinople and other hungry cities. The slave trade was also enormously profitable, both as a transfer point and as a place to kidnap and enslave people, mostly Greek Christians in this case. Genoa and Venice both depended on the Black Sea/Anatolian trade to supply themselves with horses. Finally, the region tended to be an exporter of commodities, raw goods--but an importer of the manufactured luxuries in which the Italian city-states specialized. Venetian soap was a hot ticket item. They saw in the Black Sea a market for Italian profit in general, not just a target-rich environment for merchants.

Genoa and Venice competed for particular classes of commodity, too. A great example is the materiality of cloth production. Everyone traded all kinds of cloth back and forth in the late Middle Ages. It was political as much as practical/luxurious. Genoa fought hard to dominate the alum trade, alum being used in the production of cloth. Venice kind of ceded this grudgingly-only to focus on ruling the cotton trade instead, so neither side could have a 'monopoly' on the stuffs of making fabric.

Second, the Black Sea was an important staging point. It allowed trade access to the Tatars of the steppes, but more importantly, until the mid-14th century it was a direct route to Persia. While trade with the Far East (China, India, Spice Islands) itself was considered cost prohibitive, Persia was both an access to that trade, and a direct market/source, above all for silk. Political instability in Persia eventually caused both Venice and Genoa to (mostly) withdraw from trade, to the dismay of the Persians!

And third, the Mamluks. The Mamluks ruled Egypt and the Near East from the 13th to the 16th century. They were rich, successful, a prime target for trade...and also very good at defeating Crusaders. This did not tend to bother the Italian merchants directly, who tried very very hard to secure favorable trade privileges for themselves (ideally, at each others' expense).

But it bothered the pope.

In fact, the later medieval Church tried very hard to restrict Western trade with Mamluk Egypt. At first, Church decrees-religious law, I stress-banned trade in particular goods: wood, horses, metals. The military implications of this are clear, I think. But it wasn't good enough for the papacy.

An escalating series of bans eventually closed out trade altogether. Well, legally. Of course Genoese and Venetian merchants continued to wheel and deal with the Mamluks. In both Cairo and still-relevant (but not as important as before) Alexandria, merchants from those two city-states in particular enjoyed special privileges, like the ability to dress like a local to blend in, live independently, and so forth. But the papal bans nevertheless had a chilling effect on individual merchants' willingness. This is religious law, after all. Even merchants focused first and foremost on turning a profit are fearing for their souls, a little. Genoa and especially Venice, which was more successful in worming its way into Egypt, complained bitterly and repeatedly to Rome to lift the embargoes already.

For their part, the Mamluks sought to make Cairo in particular the center of world trade. They gradually privileged it above the ports of Syria, and even eventually Alexandria as far as duties and taxes went. Yeah, taxes. The Mamluks absolutely knew what a strategic position they had. They taxed the snot out of the goods that passed through their ports between the Far East and the Latin West. The Black Sea trade offered a great way to circumvent Mamluk tariffs.

Until the rise of Timurlane put a stop to things, of course.

I believe it was still a massive shortcut to Asian markets and Russia in general. I think an arm of the silk road did converge there. It was a strong point of convergence for asian and Russian goods. Russia has rivers that connect the Baltic Sea to the Black Sea. So not just commodities flowing down but it opens trade of goods to be sold up the continent as well. Tons of money to be made.

I lack specific commodities but this is mainly because it was a thriving hub with broad access to goods from the entire Asian and eastern European regions. I mean a Doge diverted a crusade to essentially pacify Constantinople and give his state sole access to that sea. It had huge strategic trade benefits.

Bypassing the Byzantine empire in and of itself was huge. Constantinople had been the lynch pin and as such profited greatly from this trade network, essentially being the point where eastern markets meet western. When Venice secured this for itself Genoa saw the advantage and from there the two attempted to one up each other for years to come, setting up colonies further and further into the sea.

Apologies as its been a while since I read up on this subject. This is from hazy memory.

Hope someone comes with more detail. My source below was a good and quick read on Venetian history.

Source: 'City of Fortune' - Robert Crowley

So I cannot speak to the specific motivations of Venice and Genoa, other than recognizing that they were both strongly trade-based economic powers on the Mediterranean sea (relevant in a moment).

What I will speak to is the trade situation as a whole in that region at that time. There is factor at play here that significantly increased the value of maritime, ship based trade in the region; the rise of the Ottoman Empire.

The Ottomans were situated right in the gap between Europe, and the entrance to the silk road. As they rose in power, and the mongol empire declined in the region, the Ottomans more or less shut down the silk road which Europe was relying on for the past centuries.

With that trade route drying up, Europe sought other avenues for commerce. The Mediterranean was an ideal port to serve most of Europe, so if a nation could gain a monopoly of trade in the region than they would have a lot to gain economically. Both Venice and Genoa were in a position that this could become a possibility.