Antigone is arrested and sentenced to death by her uncle Creon for performing burial rites for Polynices, her brother, a traitor to Creon. Creon had decreed that Polynices's corpse was to be left out to rot and be eaten by the birds as punishment for his treachery.
Antigone is caught between following the law of the gods, which dictates that Polynices must have a decent burial, and the law of the king, which forbids her to follow the law of the gods in this matter. She chooses the higher path, which the chorus affirms as correct.
Antigone kills herself because she sees no reason to expect that Creon will change his mind about her death sentence. Entombed alive, she takes matters in her own hands. This is consistent with her character: she is a forceful person who thinks for herself and follows her own conscience. Although we are not told this and only hear of her death secondhand, we can infer she decides to cut to the chase and take things into her own hands.
Her death also represents her place as a member of an accursed family. She is the product of unwitting incest. Her tragedy mirrors that of her mother. Unlike her mother, however, Antigone is, tragically, doomed to death for following the will of the gods, not violating it. She is a symbol of those who put moral law ahead of immoral laws that states might pass.