A shortened version of grody, meaning gross, disgusting, icky, poopy, or any other word you can think of meaning distasteful or unattractive. It can also be used to describe a grody person, such as a hobo, a really ugly stripper, your ex-boyfriend, a really annoying president, or any random person you may see on the street that you'd like to casually make fun of with your friends.
Gro-gro is essentially two words, not one, which are linked together by a magical hyphen. Gro-gro can be written with or without the hyphen, but using the hyphen ensures that saying 'gro' twice is not a typo, an indeed purposeful.