What causes the yellow leaf spots that later develop a brown center on my apple leaves?

This a fungal disease called cedar-apple rust. Cedar-apple rust is a common disease of apple and crabapple. The fungus that causes the disease, Gymnosporangium juniperi-virginianae, is unusual because it must spend a phase of its life cycle as a parasite on Juniperus species, such as red cedar or ornamental junipers. Control: Grow resistant apple or crabapple varieties. Apple varieties that normally show good to excellent resistance to cedar-apple rust include ‘Red Delicious’, ‘McIntosh’, ‘Arkansas Black’, ‘Winesap’, ‘Mollies Delicious’, ‘Spartan’, …