The description is the full detailed descriptive write-up about the product. It is shown on the product page.
The description editor for the product uses the same editor as the WordPress posts and pages editor. You can use the same formatting tools and even WordPress shortcodes (even those provided by other plugins) in the product description.
The product summary is a brief 1-2 sentence description of the product. It can be used to grab shopper’s attention in the list view of a category listing, or perhaps be used as the line item description in the shopping cart and on the order receipt. By default, the summary is shown on category pages in list view.