The Jews could not hold land in Italy, so they entered the great trading piazzas and halls of Lombardy, along side the local traders, and set up their benches to trade in crops.
They had one great advantage over the locals. Christians were strictly forbidden the sin of usury). Whereas the Jewish newcomers could lend to farmers against crops in the field, a high risk loan at what would be considered usurous rates by the Church. In this way they could secure the grain sale rights against the eventual harvest.
They then began to advance against the delivery of grain shipped to distant ports.
In both cases they made their profit from the present discount against the future price. This two handed trade was time consuming and soon there arose a class of merchants were no longer trading grain, but in its stead, were trading grain debt.
It was a short step from financing trade on their own behalf to settling trades for others, and then to holding deposits for settlement of "billete" or notes written the people who were still brokering the actual grain. And so the merchant's "benches" (bank is a corruption of the Italian for bench, as in a counter) in the great grain markets became centres for holding money against a bill (billette, a note, a letter of formal exchange, later a bill of exchange, later still, a cheque).
These deposited funds were intended to be held for the settlement of grain trades, but often were used for the bench's own trades in the meantime. The term bankrupt is a corruption of the Italian banca rotta, or broken bench, which is what happened when someone lost his traders' deposits. Being "broke" has the same connotation.
There soon developed a sensible manner of discounting interest to the depositors against what could be earned by employing their money in the trade of the bench; in short, selling an "interest" to them in a specific trade, thus overcoming the usury objection. Once again this merely developed what was an ancient method of financing long distance transport of goods.
Islamic banking has the same constraints against usury as Christianity and from the same old testament notions. It will be interesting to see if, as Islam ages and matures, it relaxes its insistence that money cannot be earned from deposits held as debt.
The medieval Italian markets were disrupted by wars and in any case were limited by the fractured nature of the Italian states. And so the next generation of bankers arose from migrant Jewish merchants in the great wheat growing areas of Germany and Poland. Many of these merchants were from the same families who had been part of the development of the banking process in Italy. They also had links with family members who had, centuries before, fled Spain for both Italy and England.
This course of events set the stage for the rise of banking names which still resonate today: Schroders, Warburgs, Rothschilds, even the ill-fated Barings, were all the product of the continental grain trade, and indirectly, the early Iberian persecution of Jews.