Something that's ragged is starting to fall apart. When your favorite sweater is getting ragged, it's so worn that the sleeves are fraying.
You'll often see ragged describing clothing or a person's tendency to dress in torn, ratty clothes. Your grandmother might talk about the ragged little boy in her neighborhood, who always wears a dirty t-shirt and jeans with holes in the knees. You might put on your comfortable sweatpants only to realize they've gotten a little ragged, frayed around the waistband.