First off, we have our hero, Antigone. She is a brave girl who represents goodness and virtue. Antigone is our tragic hero and therefore must make some sort of error. In her case, Antigone's mistake is based on her love for family. She is willing to break the law in order to bury her disgraced brother, and she if noble enough to own up to the crime, even though it means death. In my opinion, Antigone is a strong heroine figure because of her selflessness and compassion. These noble traits make her downfall all the more sorrowful and tragic.
I suppose just a little bit of back story might be helpful in understanding the tragedy of this story. Essentially, Antigone's twin brothers battled it out to see who would be the new king of Thebes. They both killed each other, but because Polyneices was the rebellious brother he was not honored with burial but left to be ripped up by the dogs. Also, Antigone's egotistical jerk-of-an-uncle Kreon decided to enforce the law that if anyone tries to give the body a proper burial, they will be killed.
I found this ending rather interesting because it closely relates to one of the most popular tragedies of all time, Romeo and Juliet. In both stories we have two lovers killing themselves when they can no longer be together. The fact that this theme lasted in tragic tradition all the way from Sophocles to Shakespeare shows that love is a strong catalyst in human suffering. Throughout history, the emotion of love has strongly influenced the lives of men and women. What these two works of tragedy may be trying to teach us is that love is a powerful thing that reaches beyond death and sacrifice.