Listing Category names beside their Description is not something WordPress offers an easy solution to within the codex though it sounds easy enough. WordPress’ wp_list_categories will add the Description to the Category name link as a title tag replacing the default “View all posts filed under CategoryName”. Unfortunately we ran into this issue while building a client web site and after several hours of research into the matter and altering the core to suit our needs we at last discovered the beauty of get_categories.

Link:
WordPress: List Categories next to their Descriptions | Doc4 Advertising Agency