Grey market is an unofficial market where goods are sold that have not been obtained from an official supplier. Item brought in Grey market are not easily traceable by the manufacturer so you will have challenges to claim warranty for items bought in Grey market.
Grey market is need not be illegal in all cases. You see Flipcart selling few mobiles that are exclusive for Amazon. In this case, I remember the (Xiaomi) company India head announcing that they would not provide warranty for such purchases from unauthorized sellers.
Please feel free to counter or add more information.