The Renaissance was a historical period on Earth lasting from the 14th to the 17th centuries, centered on Europe, that was marked by rapid cultural and scientific advancement.
The period preceding the Reniassance was known as the Dark Ages. The painter Giotto helped spark the Renaissance by creating the three-point perspective. (DIS: "Die Trying")
In 2269, two Italian Renaissance paintings were in the possession of Flint: Angel Playing the Violin and Angel with Lute, both by Melozzo da ForlÃ. (TOS: "Requiem for Methuselah")
In 2370, in describing the character of Prospero to Lieutenant Commander Data, Captain Jean-Luc Picard noted that "Shakespeare was witnessing the end of the Renaissance and the birth of the modern era, and Prospero finds himself in a world where his powers are no longer needed." (TNG: "Emergence")
The term "Renaissance man" was sometimes used to describe a great thinker with a large body of knowledge. In 2374, when Lieutenant Commander Tuvok expressed his appreciation at the detail of the maps created by a holographic re-creation of Leonardo da Vinci, Captain Kathryn Janeway explained "He was a Renaissance man, Tuvok. Interpreted, reinterpreted, deconstructed, fantasized about all through history." Later, as Janeway and the hologram prepared to take flight in a revised version of his glider, he commented "When Petrarch climbed Mont Ventoux and saw all Europe below him he knew he was witnessing the birth of a new age. He was witnessing the Renaissance. The rebirth of our world! So, Catarina, at this summit here, you and I will be reborn. Reborn, with wings!" (VOY: "Concerning Flight")
In the story outline for TOS: "The Cage", one of the episode's many illusory scenes was to have been in Renaissance Venice, featuring "a palace at the edge of the old city's central piazza." (The Making of Star Trek, p. 53)