The Hunger Games is a dystopian fiction that revolves around the character Katniss Everdeen. The story takes place in the nation of Panem, which has a wealthy central capital and twelve outlying districts. Each district has a specific purpose that serves the capital, such as farming, coal-mining, and so on. The people of Panem must abide by very strict rules, such as staying within their district, working their district's resources, and participating in the yearly Hunger Games. Due to a past rebellion, each district must choose one boy and one girl to “sacrifice” for the Hunger Games, a game where the participants must fight to the death until only one remains.
Of course, in this harsh world, there are rebellions. The Hunger Games came from a large rebellion in a time called the “dark days,” in which District 13 was destroyed. In order to control and prevent future rebellion, the president created the Hunger Games. The Capitol also uses military control to keep the other districts in check. If a person is found to be trying to escape their district or rebel against the Capitol, they are turned into an Avox. An Avox is basically a slave who has had their tongue removed. They are not allowed to interact with anyone, and they serve the Capitol for the rest of their life.
When she arrives at the Capital, Katniss recognizes an Avox in her room as a redheaded girl she saw in the forest. If you remember, at the beginning of the story, Katniss and Gale were poaching over the fence around District 12 when they witnessed a redheaded girl and boy trying to escape toward District 13. The boy is harpooned, and the girl is captured by a Capital flying vehicle. The redheaded Avox is the same girl Katniss saw trying to escape.
If Katniss showed that she knew this Avox, she would have to explain how she met her. At the time, Katniss was illegally over the fence of her district poaching for food. In turn, she would be considered a traitor or rebel for having broken the rules.