The Cornucopia is the central point of the arena and the location of the event of the bloodbath that occurs on the first day of the Games. The Cornucopia tends to house supplies that can be useful in the arena, including weapons, food, shelter, water, etc. It is shaped like a horn and can be useful in the means of protection and shelter during the Games. As an example, Foxface used the Cornucopia as a house for an amount of time before the Feast occurred.
It is important because it tends to be where a majority of the arena action takes place, whether it be the event of the Bloodbath or the Feast.