Antigone commits suicide by hanging herself, but the roots of her death lie in following the moral law of the gods rather than the immoral law of her uncle, Creon.
Creon has decreed death to anyone who buries Antigone's brother Polynices, who rebelled against Creon in a civil war. Creon wants Polynices's bird-eaten, desecrated corpse to act as warning to other Thebans not to challenge the state.
Antigone understands this violates Greek custom and the law of the gods that demands that every Greek get an honorable burial. She ritually buries Polynices, knowing this will anger Creon and most likely lead to her death, but she insists on obeying a higher law than Creon's.
Creon sentences her to be entombed alive. His son, Haemon, who is betrothed to Antigone, the wise seer Tiresias, and the chorus all speak out against this as an outrage against Antigone. However, Creon, like Oedipus, suffers from the tragic flaw of pride or hubris and won't listen to advice until it is too late. When he does finally rescind Antigone's sentence, she is already dead by her own hand. As a result, he loses his family, as both Haemon and Euridyce kill themselves. Creon is left broken, with nothing to live for.
Antigone's brave stand against her uncle and her courage and agency in choosing the time and means of her own death have long been used as symbols of social resistance and the honor of placing one's conscience above a state's immoral laws.