Something that's localized only affects a specific place or part of the body. Localized numbness in your fingers means that only your fingers feel numb — the rest of your hand and arm feel normal.
You'll often hear the adjective localized in the context of medical symptoms, treatment, or diagnosis. Localized pain exists in one part of your body, and a localized infection is also restricted to one area — it hasn't spread to other places in the body. Another way something can be localized is simply to be local, like a localized radio station or a localized source of food for school lunches.