Historical periods overlap, and it's always dangerous to assign eras a specific title, as though one particular movement was the most important. The Renaissance is a perfect example: some historians even argue that the Renaissance wasn't a period as such, but rather an artistic and intellectual movement within the broader context of the Early Modern Period.
The problem with this view is that it assumes the Middle Ages which preceded the Renaissance were a "Dark Ages" epoch that was anti-intellectual and steeped in superstition, and that needed rescuing by the more sophisticated thinkers of the Renaissance. Of course, there are plenty who see the Renaissance as a step backward, that it was a reversion to Classical ideals.
Which is partly true, too. The term itself means "re-birth," and it was a hearkening back to the era of Plato and Aristotle, an embracing of artistic realism and ancient literary forms, above all a movement toward blatant humanism. Whatever you call the period—the first stage toward Modernism, a merely cultural movement, or an epoch unto itself—it's undeniable that it initiated a move away from Scriptural authority toward a reliance on human reason as the arbiter of truth and knowledge.
Foundations for this kind of thinking had already been laid in the work of Thomas Aquinas. A Catholic theologian, he upheld the Bible as the source of all knowledge concerning God, but (fairly arbitrarily) asserted that another authority ought to be appealed to in matters of "human" knowledge. This included history, philosophy, science, art, etc., and meant that spiritual and earthly knowledge were effectually separated. His secondary authority was Nature, as opposed to the spiritual realm of Scripture.
Renaissance thinkers held onto this dichotomy, treating God's Word as just another book of wisdom, useful for its subject matter but not pertinent for the pursuit of other knowledge. By isolating Scripture this way, these new humanists were able to pursue non-religious interests without relating it to the Gospel or the Christian life. Knowledge became partitioned, and almost wholly secularized.
Modernist historians do something funny at this point. They act like this was a liberation from the oppressive, Dark Ages Christian indoctrination perpetrated by the Church prior to the advent of the Renaissance. Many cite Galileo's fight for scientific truth as a fundamental example of what they suppose to be religious oppression in the face of rationalist progress.
What they usually fail to acknowledge is that it wasn't Church doctrine Galileo was arguing against, but ancient Greek astronomy a la Aristotle; the powers that be had simply assumed, in the wake of Aquinas, that Aristotle was the final word on knowledge. So it wasn't religiously inspired ignorance Galileo was up against, but the beginnings of the humanism the Renaissance held in such high esteem.
Christian thinkers have often pointed out that only the Christian religion allows for completely free study of any intellectual topic. The case of Galileo (himself a Christian) would seem to support this; while it's true that the Catholic doctrine of Church tradition had led to the cementing of Aristotelian science as doctrine, it's also true that that was a biblically unjustifiable stance, regarding both tradition and scientific inquiry.
The Renaissance wasn't just about science, however. It was about art, history, poetry, and every other human pursuit. The humanists sought to recover the Classical ideals of human nobility and reason, and to use those as the basis for a revitalization of everything from architecture to painting to music. A Renaissance man excelled in a variety of things, and in this way established his autonomy.
One of the constants of human history is man's rebellion against God. It was no different in the Renaissance, and the philosophies that arose during the period gave rise eventually to the solipsism of the Enlightenment, which went the Renaissance one better by claiming man could know nothing that his own reason and logic could not comprehend without any outside aid or authority.
Fortunately, the Renaissance wasn't the last word. The Reformation which followed close on its heels was based on the biblical assertion that it is only through God that we can know anything, and that all human knowledge is subject to the truth of His Word. This was another kind of rebirth, a re-birth of God's people in response to the faux re-birth of the man-centered Renaissance era.