Unpeeled garlic cloves in French / Belgian cooking?
Unpeeled onions and garlic help thicken liquids (just a little).  The skins of onions and garlic are at least 10% pectin, the substance that is used to thicken jellies.  If you are making a stock or a soup, you can place the washed unpeeled garlic or onion quarters in an oversized herb sachet.  After cooking you remove the sachet and discard its contents.

The skins have also been found to be rich in antioxidants.  You can read all about the science of garlic and onions in Garlic and Other Alliums.  While it does discuss the antioxidant effects of Alliums in general it does not treat the particular compounds that have been discovered in the skins.