From CNA:
According to the ancient Church historian Eusebius, while Jesus was still alive, the ruler Abgar V of Edessa was afflicted with an incurable and painful disease. He had heard of the miracles of Jesus and wrote him a letter requesting a visit. Jesus responded that he would send one of his disciples.
After Jesus’ ascension into heaven, Jude went to evangelize near the city of Edessa and went to visit Abgar. Jude laid his hands on the sick ruler, and he was reportedly instantly healed. Many people choose to carry the image of St. Jude on a medal or as a pendant on a necklace for comfort and call on him in their time of need and healing.