In the novel The Hunger Games, the Capitol uses the games to control the people of the Districts.
The main reason the Capital can use the games to control the people of the Districts is fear. The people of the Districts are fearful that if they revolt against the Capitol, in protest of the Games, that the Capitol will destroy their respective districts as they had in the past with District Thirteen.
The Capitol uses District Thirteen to remind the other districts that they hold and maintain power given they can destroy any district at any time.
Another way the Capitol could maintain power over the districts is by withholding supplies from them. While this is not stated in the first novel, is is certainly inferred by the way the people are fearful of losing the supplies that they need to survive. As one gets further from the Capitol, it is apparent that the districts become poorer. The Capitol uses this fear to suppress any revolts which may come about as a result of protesting the games.
Every year a boy and a girl from each district is picked and chosen to participate in the Hunger Games to fight to the death which is broadcasted nationally. This happened after District 13 rebelled against the Capitol in history. The Capitol does this barbaric act to prove the consequences of a rebellion and how the other districts are powerless.