What new ideas and techniques resulted in more realistic and accurate portrayals of people in Renaissance paintings?

There is a major difference between the portrayals of human figures in early Renaissance paintings and frescoes (think, for example, of Giotto's The Gift of the Magi and Fra Angelico's The Anunciation) and those which emerged in the 1480s, starting particularly with Botticelli's work. The earlier works mimic the conventions of the Middle Ages, in which figures are rather identical, two-dimensional, and have elongated bodies. More notably, babies in these paintings look like miniature adults.
Later Renaissance artists, however, took an interest in Classical and Hellenistic sculpture. Their predecessors had eschewed the Classical world, due to associations with behavior that the Catholic Church deemed sinful. Humanism, a philosophy that encouraged the view that the human body was not the source of sin but a thing of beauty, resulted in more attention to and appreciation of the human form. Classical sculptors depicted the diversity of the human body in all stages of life. They depicted its dynamism, too. Consider, for instance, Laocoon and His Sons as an example.
The scientific revolution also took place during the Renaissance. Studies in anatomy, especially those by the Belgian physician and anatomist Andreas Vesalius in the 1500s, would give painters and sculptors a greater understanding of the human body.