The main source of conflict between Antigone and Creon is over the burial of Antigone's brother Polynices. Some background information is needed at this point. There is a civil war between the two brothers of Antigone - Polynices and Etocles. Creon is opposed to Polynices, because he attacks the city of Thebes to take over. In fact, Creon states that no one should mourn or bury the body of Polynices, but that the body should be left out to rot and be devoured by animals.
In light of this, Antigone is in a dilemma. Does she listen to the law of the land and risk her life, or does she act piously towards her brother to bury his body. This is the conflict that is in view. Antigone decides to bury her brother, but she is caught and sentenced to starve to death.