Florence was one of the largest, if not the largest, city in Europe in its heyday in the 1200s and 1300s, reaching as many as 100,000 people. While that seems small by today's standards, the world population was much less then, and Florence was known as a mega-city because of its size, wealth, and influence.
Banking and cloth manufacture were both important industries in the city that made merchants wealthy. However, the city is most renowned as a financial empire, with the Medici family at the forefront.
The Medicis did not invent double-entry booking, in which both profits and debts are tracked in the same place so that a company can quickly assess its bottom line and know what is bringing money and what is causing it to flow out again, but they made this innovation an essential component of their business model. This way, they were able to keep close track of their business operations and maximize their profitable endeavors, becoming very wealthy.
In addition to this, the Medicis pioneered letters of credit. While lending money at interest, called usury, was banned by the Church, letters of credit allowed the Medicis to skirt this ban. Most merchants didn't want to carry large amounts of cash across Europe, due to unstable conditions and fear of robbery. Instead, they would put the money to pay for goods in a Medici bank and carry a letter of credit that the seller could then cash like a check. The Medicis charged a fee for this service that merchants were very willing to pay for the convenience of the system.
Fortunately for us, the Medicis invested much of their wealth in the arts, allowing the new ideas of the Renaissance a place to flourish.