This probably should be in the 'herbalism' category.
Alligator pepper and grains of paradise are the same thing, nicknames for, as Raven said, Aframomum melegueta.
They are in fact spices, with a peppery taste. In parts of Africa, they use alligator pepper for digestion issues, and I hear they are also used for divination. I also hear it is used in Voodoo, however I am not sure what for.
Apparently it also has great healing properties, especially when it comes to dealing with bacteria.
If you are wondering about their metaphysical properties, here is what I got from a site (http://www.scribd.com/doc/2413680/Herbs-and-Their-Magickal-Properties):
Grains of Paradise: Lust, Luck, Love, Money, Wishes.
I know this may seem surprising, but if you research you'll find information. -.-