In what ways did the art, architecture, and literature of the Renaissance reflect new ideas at the time?

This is a huge question, but in general terms, the Renaissance was a time of rebirth of interest in the art, thought, and literature of the Classical Age of Greece and Rome. Writers such as Aristotle and Plato were beginning to rival the Bible in influence. There was a burst of interest in Greco-Roman myths. Educated people were beginning to learn Greek as well as Latin.
This is reflected in a move in art during this period away from purely Biblical themes. We see ancient mythology enter into major paintings such as Botticelli's Birth of Venus. Literature begins to celebrate humankind as the glory of God's creation and not simply as fallen sinners. Writers such as Dante incorporate classical figures, such as Virgil, into even religious works such as The Divine Comedy. Writers such as the ancient Roman author Ovid provide source material for Renaissance authors.
In architecture, we see a move away from the Gothic to more rounded and balanced designs based on Greek and Roman models. Many of Florence's buildings, for example, have domes rather than tall spires and are based on Roman buildings.
Overall, the influence of ancient Greece and Rome are evident in Renaissance creative arts.