"Flat" is not an official term, but has been used to describe a category hierarchy that does not contain multiple levels of subcategories.
For instance, Category:Regions is a "deep" hierarchy containing many subcategories, with each subcategory also containing multiple levels of subcategories, etc. You can navigate through multiple levels before reaching a category where we would categorize profiles.
A category structure like you may find an ONS Project is typically flat, where there are very few levels to navigate through.
If you have a specific question on categories, let me know!