The Long Description will display on the product detail page when the product is selected. The Short Description will display under the product name in the product selection page. For the Long Description you will use the Text Editor to enter text, images, links, tables, etc. Click here to download a PDF on using the text editor.  while the short description does not have those same customization capabilities. 

The image below shows where the Product Long Description will display on the product page. Depending on the skin you choose, it may look different. 

The image below shows where the Product Short Description will display below the product icon on the category page. Depending on the skin you choose, it may look different but always displays below the product icon.