Things that are fragmented are broken into very small pieces or divided into factions. When voters are bitterly split, unable to find common ground, they are fragmented.
You can describe the ancient shards of pottery at an archeological dig as fragmented, or the pieces of the bowl you just dropped on the kitchen floor. It's also good for talking about something that doesn't form a coherent whole: "The movie's fragmented plot made it hard to understand," or "The whole country is fragmented, and this election isn't helping matters." The Latin root, fragmentum, means "a piece broken off."