Depends upon the context. Literally, it refers to something that has become unfastened or has fallen apart. For example, if the clasp on your necklace breaks, you would say "My necklace has come undone." Or if you have to stop and tie your shoe: "Wait a minute, my laces have come undone again."
Sometimes the phrase is also used to describe someone who loses their temper or composure, or who completely breaks down emotionally: "I told my husband that I scratched the paint on his new car, and he totally came undone."