The primary category you select for an item determines the breadcrumb for the search result of the product or content detail page. If no primary category is set for a product, the classification is used to determine the category links.
For example, if a customer searches for boots and selects a man's boot from the results, the breadcrumb for the result shouldn't point to a category that is too broad, such as shoes, or one that isn't applicable, such as women's shoes.
The classification you select determines the attributes shown for the result. If no classification value is set, the attribute value is taken from the primary category.