When an item is passed and saved into Shopify, a description is included as you can see in this screenshot of a product in the admin:
The product description is not included by default on the Shopify cart page of most themes. To add the description, you can add the variable {{ item.product.description }} to cart_template.liquid under Online Store -> Themes -> Edit Code -> Sections
Please contact Shopify if you need more help customizing your theme.