This is a good question. Some background is important to answer this question. There is a battle between Antigone's bothers Etocles and Polynices. Polynices, in fact, attacks the city of Thebes to take it over. In that battle both brothers are killed, but Creon the ruler of Thebes says that no one must bury Polynices, because he has attacked the city. They must allow him to die unburied and eaten by the dogs. Within this culture, being unburied was one of the worst things that could happen. Your soul, it was believed, would never find rest.
In light of this, you can begin to see the dilemma. Should Antigone and Ismene bury the body? Antigone says "yes," even if they should die. Honor compels one to risk one's life to do what is right. Ismeme says, "no." After all they are only women and they should not be breaking the law. These are two different stances and the source of the conflict.