Prior to the Renaissance artists were less concerned with the illusion of reality and more concerned with the content and symbolism of their work. The size of each element in the image related much more to its importance, rather than it's placement in a space.
Artist unknown. Madonna and child.
Notice how large the Madonna and child are compared to the rest of the image.
Artist unknown. Garden Scene.
Look at this image, examine its composition, how is perspective used in this picture? What is the most important element? how can you tell?
By the height of the Renaissance, artists had mastered the mathematics and visual techniques of perspective. Artists such as Brunelleschi, Leonardo DaVinci and Piero della Francesca were using it to great effect, giving their work a stronger illusion depth.
Piero della Francesca. St. Anthony's Polyptich (detail)
Brunelleschi devised the method of perspective for architectural purposes -- he is said by Manetti to have made a ground plan for the Church of Santo Spirito on the basis of which he produced a perspective drawing to show his clients how it would look after it was built. We can compare this drawing with a modern photo of the actual church.
Brunelleschi, Drawing for Church of Santo Spirito.