A cure is a treatment that ends an illness or makes you feel better. There is no cure for the common cold, or for a broken heart. Waaaaa.
Many researchers focus on finding cures for diseases like cancer and diabetes — while it is possible to recover from incurable illnesses, it's not possible to cure them. You could also say, "This Florida winter is going to cure me of missing Minnesota!" When someone cures meat or fish, they smoke or salt it to preserve it. The Latin root is curare, "take care of."