Ideally, you will never delete a product. Deleting the product erases it permanently from the site. If a product has been purchased, it cannot be deleted. Reasons for this range from someone may need to find it for documentation to keeping track of the growth of the community's shops.
If you retire a product, it will stay on your profile, but cannot be purchased. Retiring a product helps your store still come up on search engine queries, site searches, and the like.
When you are editing one of your products on the bottom right corner you will see two options, Retire and Delete: