I am having trouble understanding the Renaissance revival of ideals and aesthetics from Greco-Roman antiquity. What did this mean in practice?
The Renaissance revival of classical antiquity was extremely complex, affecting almost all facets of religion, the humanities and the arts. The key concept holding these diverse elements together was the notion of the return "ad fontes" (to the origins).
In religion, the return to the origins of Christianity was a cornerstone of the Protestant Reformation, which argued that the Roman Catholic Church had moved away from Christ's teachings. First, the Bible used in the Roman Catholic Church in the Middle Ages had been Jerome's Latin translation (known as the "Vulgate"). Reformers (including some Roman Catholics) during the Renaissance strove to reconstruct the original Hebrew of the Old Testament and Greek of the New Testament. Protestants also argued for individual reading of the Bible, independent of the later body of doctrine built around it by the Church Fathers.
In the humanities, the first element of the return to classical antiquity was linguistic. The Latin spoken in the church and used in most writing in the middle ages was "vulgar" Latin, quite different from that used in classical authors. With the rediscovery of more ancient texts, and especially Cicero's letters, the humanists of the Renaissance attempted to restore a more pure form of Latin in the schools and in learned discourse, in a movement known as Ciceronianism.
Next, in the arts, rediscovery of classical models lead to several stylistic changes. In architecture, Andrea Palladio's reading of the Latin architect Vitrivius led to an interest in simplicity and harmony, as opposed to the earlier Gothic. Many Renaissance dramatists returned to classical models for inspiration, with the revenge tragedy especially influenced by Seneca, and Aristotle dominating literary theory.