Something that's distressing makes you feel sad, upset, or worried. A distressing phone call from your dad might involve him telling you your grandma is in the hospital.
When something causes distress, "anxiety, sorrow, or pain," you can describe it as distressing. Both words come from the Vulgar Latin districtia, "restraint, affliction, or narrowness," from distringere, "draw apart or hinder" in Latin. Distressing headlines in the newspaper convey terrible news, and distressing text messages from your friend might make you worry for her safety.