Answer:
To remind the rebels that if they go against the capitol, they will suffer.
Step-by-step explanation:
During the "Dark Days," there was an ongoing war between the Capitol and District 13, they were rebelling. The Capitol was much stronger than District 13, but District 13 also was the district to manifacture nuclear weapons. So they made a treaty. If District 13 pretended to be wiped out and not resurface, then the Capitol would leave them alone.
This lead to the Capitol realizing they needed a way to control the districts without them rebelling - to scare them from rebelling. So they came up with the Hunger Games. Games where 24 children would fight to the death and only one would survive. It served as a purpose to "remind the rebels" that their children are suffering because of their actions.