The major conflict is between all of the districts and the capital; during the entire book, these two main groups are fighting with each other. The conflict is over who will gain control in the end--will it be the materialistic capital who has been in charge for so long now, oppressing its people and using them for slave labor? Or will it be the leadership of District 13, who have been staging a rebellion for years? It is through this conflict, that is played out in District 12, Disctrict 12, and the capital streets itself, that is such a good showcasing for rather serious themes of war, violence, power and greed that are evident throughout the book.
Minor conflicts erupt between Katniss and various characters throughout the book, but the major conflict lies in the larger picture of the battle for power between the districts and the capital. I hope that helps; good luck!