Thank you for your question.  Your apple trees have cedar-apple rust.  This is a plant disease caused by a fungus that spends part of its life on juniper/red cedar trees and part of it on apples and their other members of the apple family.  Cedar-apple rust can't be cured on the current season's apples or leaves.  Fungicides don't cure, they only prevent.  So plan now to spray with a preventive fungicide like copper or sulfur next spring when the buds turn pink, when most of the petals have fallen and again 10 days later.  This link will tell you more about rust diseases.  I hope this is helpful.
http://plantdiagnostics.umd.edu/level3.cfm?causeID=1195

Ok. Thanks so much for your help!

You are most welcome.  I'm glad I could help.