A “neutral shoe” means that it is made for someone with a neutral walking or running gait or someone who supinates (someone who rolls their foot outward). This is also called underpronation. If the wear on your sneakers looks even on both the inside and outside heel, you are probably a neutral runner. It's kinda like Switzerland where you don't take either side. Not sure? Take a quick test here.
Shop here for neutral running shoes. Your local New Orleans running store has the best selection in neutral running shoes. Shop online with free shipping.