One of the Reaping Balls.

"She reaches in, digs her hand deep into the ball, and pulls out a slip of paper."
Katniss Everdeen describing a name being picked out of a reaping ball during the reaping.[src]

The Reaping Balls hold the slips of paper with the names of children from age 12 to age 18, to be possibly reaped in from each district. There are two Reaping Balls, one for boys and one for girls. During the reaping, the reaping balls are placed on a stage placed in front of the Justice Building for the district escort to choose a name from each.

The Hunger Games

RB 1

The Reaping Balls during the 74th Hunger Games reaping.

During the District 12 reaping for the 74th Hunger Games, Effie Trinket was the escort who picked the tributes. She chose Primrose Everdeen from the girls' ball. However, her sister Katniss Everdeen volunteered for her. Effie then chose Peeta Mellark from the boys' ball.

Catching Fire

During the 75th Hunger Games, the third Quarter Quell, the twist was that only past Hunger Games victors would be
Cf peetaeffiekatniss

Peeta, Effie and Katniss beside the Reaping Balls.

eligible to be reaped.

In District 12, being that there were only three victors alive: Katniss, Peeta, and Haymitch Abernathy, Effie had to claw around the females' ball for a few minutes, despite there being only a single slip of paper with Katniss' name in it. She then chose Haymitch out of the males' ball, but Peeta immediately volunteered in his place.