Basically, it's similar to the grayfox cowl, but with two main differences: 1- when you wear the hoods,your crime gold starts at zero, meaning the guards won't start chasing you instantly cause you are the gray fox or whatever! you're just a nobody with a clean slate!   2- when you remove the hood,all the crimes you committed while wearing it will be forgiven and forgotten! so you can wear it again and do all of your dirty deeds all over again! :p
you can also use these hoods to hide from the law,if you are a criminal, wear a hood and walk right past the guards and they won't recognize you!
the hoods come in several colors so you can wear them with any armor or set of clothing. you have silk hoods and tattered hoods, black hoods and white hoods... 
buy the hoods from the "three brothers..." shop or the the "good as new" shop in imperial city market. 

NOTE,all of these hoods function similarly, the difference is only in their color or fabric...
NOTE, when you are in a fight with the guards, don't remove your hood, because even though your crimes are forgotten, the guards won't stop fighting you,and if you resist when you're not wearing the hood, you will be responsible for attacking the guards and will be jailed or fined, just leave the area or end the fight first,then you can safely remove your hood

Have fun you criminal scums! lol  go ahead and violate the law under any guard's watch (and get away with it)! :p