If something is localized, it happens inside a small area and does not spread far. A localized infection stays in one part of the body. A localized storm hits one valley, not the whole island. Doctors and weather people use this a lot, because the first question is often “is it here only, or everywhere?” Though actually, localized does not mean small and weak. A problem can be fierce and still be localized. You will also see the word in software: a localized app has been fitted to a language and a place (Taiwan Chinese, for example). That is a different job of the same spelling — made local, rather than kept in one spot.