Grief mode is the brand new mode introduced in Call of Duty: Black Ops II zombies. It allows 8 people to play at a time, but they are against each other with up to 4 players per team. The goal is to survive the longest, and let the other team die before your team does. The game-play is the same thing you have come to know, with the same perks, power ups, etc. There is one new power up, commonly referred to as the "Meat" power up, it is a piece of meat, that, when grabbed, it will replace your gun with a piece of rotten meat. It is used to mess with the other team, as whoever gets hit by it has a monkey bomb effect, where the zombies ignore everyone but the guy that got hit with it.
Both teams can also shoot and knife their enemy team. When they do this it will push the players.