Featured Categories option allows you prioritize some Item Categories to be displayed in breadcrumbs of Item post detail page and in the lists of Item posts like search results, Item Category or Item Location pages. Option is helpful when your Item post is assigned to many Item Categories so result on the page may be the mess of all categories displayed on the page as you see on following image (images are from Directory+ theme, the same apply for other themes that include Featured Categories option):
How it may looks if for example just two Item Categories are defined as Featured Categories:
Option Featured Category is available for each edited Item Category:
In Theme Options > Item Categories/Item Locations section you can define number of Item Categories that are displayed in breadcrumbs and search results with Item posts. Option defined to 0 (zero) means that Featured Category option set for categories is ignored and displayed are still all categories.