When things are scattered, they’re spread out all over the place. If the forecast calls for scattered showers, it’ll rain here and there.
Items lying at random intervals and at some distance from each other can be described as scattered. Your birthday cake might be scattered with sprinkles, and the floor of your little sister's room might be scattered with Lego blocks. Another meaning of scattered is "messy" or "disordered" — you can describe yourself as scattered if you're feeling disorganized and confused. The word scatter is probably related to shatter, "break into pieces," from a Middle English root.