They go back for what is called a Feast. Occasionally, to make the games more interesting, the game makers will put something each contestant desperately needs inside the cornucopia and they all can go and get it, usually resulting in a large fight.
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Katniss first went back to the cornucopia because there was a feast, where every district was given something they needed urgently
Katniss urgently needed some medicine for Peeta, because he had blood poisoning and his wound was infected.
Peeta, Cato and Katniss later when back to the cornucopia to finish The Hunger Games, to participate in the final fight, where Cato dies and Katniss and Peeta are both crowned victors.
They have trackers that were inserted into the tributes arms.
The Cornucopia represents the Harvest the Districts have after each Hunger Games. The Cornucopia is shaped like a horn with round edges and is gold, that's shining brightly.
Haymitch told Katniss not to go to the Cornucopia at the beginning of the Games.
The cornucopia is basically a big horn. When the tributes enter the arena, their platforms surround the Cornucopia which holds supplies to aid the tributes in their survival. It is also used as shelter and protection by some, a hiding place by Foxface, and a safety zone by Katniss, Peeta and Cato.
The Quarter Quell! In this, all the winning tributes from a district are put back in the drawing for the Hunger Games so that when the tributes are picked, it is from a pool of winning tributes.