In what situation could we use black garlic?
EDIT: Black garlic starts out as regular garlic and is put through a fermentation process that besides changing the color of the cloves to black, also mellows the flavor and reduces the sharpness associated with raw garlic.  The texture of the cloves become very soft, also.  While I have never used nor eaten black garlic, a website, linked below, is dedicated to everything related to black garlic, including how to use it in recipes.

Blackgarlic.com has a wealth of information on how this fermented version of garlic is made, its unique qualities including taste, texture and chemical properties, where to get it and...recipes!

http://blackgarlic.com/

NEW EDIT: And to balance out the linked info. so there's a non-commercial reference, I found this very in-depth article on black garlic's attributes that includes a reference to a scientific study: http://www.wellbeing.com.au/newsdetail/Black-Magic-Garlic_000553