During the Renaissance, Italy was a collection of city-states, each with its own ruler—the Pope in Rome, the Medici in Florence, the Doge in Venice, the Sforza in Milan, and the Este in Ferrera. Among the ruling families of these city-states there was unceasing conflict and intense rivalry, either by open warfare or, in times of peace, through economic and artistic competition to achieve the most brilliant court. The Republic of Florence (Firenze) was the richest of them all and even the richest in all of Europe because of its successful cloth trade and because the richest banking house operated there. The Medici family, therefore, consisted of arguably the most powerful people in all of Europe at that time, rivaled by the Albizzi, who constantly contended with the Medici for power.
There is a very good PBS documentary called The Medici: Godfathers of the Renaissance, from which you can learn a lot more about the ruling family of Florence—and the narrator's voice in it is hilarious. Basically, the Medici are all over this time period. They started from humble beginnings, however; they started out primarily as working-class bankers and moved up to power. And you'll see the extent to the Italian phrase amici del amici ("friends of friends"). Brunelleschi, friends with Donatello, was the house architect for the Medici, and Leonardo da Vinci was apprentice to Lorenzo de Medici—just to name a few names. The Medici were generally the ones who commissioned the great artists to produce their masterpieces (and add in propaganda images to promote the Medici and Florence—Benozzo Gozzoli's fresco The Procession of the Magi is the prime example of this, sending the message of Medici supremacy).