I don't know much about the 'arts' side of the Renaissance, but looking at texts and works of classical literature, you cannot really see it as a rediscovery. The Renaissance and humanism are (I think) very closely linked and a lot of the classical culture which permeated into high court culture in the Renaissance was a result of humanism. The main aim of humanism was to provide literary clarity: they placed huge emphasis on good translation of latin, greek and hebrew.

So, in a sense, it was a 'rebirth' of classical culture in so far as it was a more accurate account of certain texts. Obviously, the major one of these was Erasmus' bible, which was translated into latin from the original greek. I would like to respectfully disagree with the guy who commented first; the church was never more powerful than in the 14th, 15th and 16th centuries and 'secular ethics' was seen as heresy. The extent to which they admired classical figures is also questionable: they had to rationalise using Plato and Aristotle's works by saying that, if they were born in the 15thc, they would be Christian. But mostly, the revival of antiquity should be seen as a small, educated sub-sect of society who admired the Latin and Greek that these people wrote and sought to emulate it.

--Not a true Historian, but took a class on this.

Basically it boils down to the erosion of the Catholic Church. Simony, selling of indulgences, the Avignon Papacy (there were 3 popes at one point and one of them was headquartered in France), and even the Black Death (it was so devastating and the Church wasn't providing any answers) got people questioning the ethical legitimacy of the Church running everything. So they started thinking in terms of secular ethics as a ruling guide for society. And this being largely started in Italy, the Italians had a certain pride in the old Roman Empire so they started re-examining guys like Cicero and Virgil and drew on that.

Start looking at Petrarch, Boccaccio, Alberti, and Dante to see more on the start of it.