In "The Hunger Games", the districts represent the poor subservient masses that are ruled by those inhabitants of the Capitol. The 12 districts and the Capitol together form the country of Panem in the novel. The name "Panem" comes from the Latin phrase "panem et circenses," or "bread and circuses."
The Latin phrase connects the country of Panem in "The Hunger Games" with that of ancient Rome. The hunger games themselves can then serve as a metaphor for the Roman gladiator games. The symbol of the districts as being a representation for the poor masses is substantiated by the fact that the vast majority participants in the games are drawn from Panem's districts rather than the Capitol. The reason for this is that the participants receive extra food for their families if they win, and in the districts, where the inhabitants are starving, the games are one of the only opportunities to survive.
The hunger games were also created in order to punish the people of Panem's districts. At one point, during the time referred to as the "Dark Days" in the novel, the districts revolted against those in the Capitol. The Capitol put down the revolt by destroying one of the then 13 districts and by defeating the other 12. From that point on, the poor were contained in the districts, while the wealthy lived in the Capitol.