A corporation is a separate legal entity that has privileges and liabilities that are different from that of its members.
Examples of Corporations found in video games:
Umbrella Corporation consists of a large bio engineering company that creates many products such as medicines. The company is secretly a very large power, but hides it by creating a powerful public face. They are known for creating a deadly T-Virus that dramatically alters living and recently deceased beings. This corporation plays a huge role in Resident Evil.
Shinra Electric Power Company is a ruthless mega-corporation that harvests Mako, the life force of the planet Gaia, and transforms it into electricity to power the city of Midgar and its surrounding area. In Final Fantasy VII, Shinra serves as an antagonist organization to the player's eco-terrorist group Avalanche.
Aperture Science was a large corporation that died out slightly after the leader if it, Cave Johnson, died from moon rock radiation and a robot named GLaDOS took over and murdered almost every human in the building. The corporation shows large amounts of power, as suggested many times, the ruler of the world and the combines find themselves unable to enter, making Aperture Science one of the most powerful forces in the Half-Life/Portal world.
Abstergo Industries is a company that is credited with many technological advancements. As quoted by a character from Assassin's Creed: "We change the world. Every day, in a hundred different ways." The group secretly is after a group called the Assassin Order.