There's no surprise in the fact that Antigone, the sequel to Oedipus the King, is a tragedy. It's only fitting that the continuation of such a dark, tragic tale be just as full of suffering and sorrow. 

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.
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Antigone caught in the act of burying her disgraced brother
So all that said, what makes Antigone a tragedy is all the death that takes place because of this in the tragic outcome. First, after she is caught, Antigone is sentenced to die by being sealed in a tomb and left to starve. When Kreon's son Haimon (who is also Antigone's fiancé) hears of this, he breaks into her tomb to rescue her, only to find she has hung herself. In response he kills himself, and then his mother kills herself out of grief. So in short we have one big suicide party going on down at Thebes.  In all seriousness though, I believe this ending is meant to teach the reader specifically about love.
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.

 
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Joseph Krutch 
gives us a strong idea of his definition for tragedy in his essay "The Tragic Fallacy"

Krutch spends a lot of time specifying what tragedy is not. First, it is not an "imitation of noble actions" as Aristotle once said. This is because: a) true art cannot be defined as an imitation but an adaptation, and b) the concept of nobility is too abstract and holds different meanings for each person. I agree with this because a genre such as tragedy, which is enjoyed by people of all backgrounds and beliefs couldn't have become so popular if it were based on controversial ideas such as nobility. People must relate to tragedy somehow for it to be so well loved. And not all of us can relate to the same definition of nobility.


    Krutch goes on to show us just what it is we can relate to in tragedy, and that is a “celebration of human greatness". Tragedy is not a dark gloomy genre, but is in fact "an expression not of despair, but of the triumph over despair and of confidence in the value of human life." What I concluded from this is that tragedy may include sad or depressing situations based on the fact of human suffering, but it does so in order to show us that humans possess the passion, power, and perseverance to come through that suffering. Essentially, it's a testament to how capable we are.

    One last point that "The Tragic Fallacy" makes is that tragedies still have "happy" endings. This may seem farfetched due to the fact that tragedy is characterized by suffering, but Krutch explains this statement clearly:
     "Whatever the character of events, fortunate or unfortunate, which they recount, they (the authors) so mold or arrange or interpret them that we accept gladly the conclusion which they reach and would not have it otherwise."

    Essentially, even though it's sad that Juliet kills herself (for example), we as readers can be satisfied with the strong act of passion, strength, and meaning her death holds. As Krutch says:"We accept gladly the outward defeats which it describes for the sake of the inward victories which it reveals."
    So even if tragedies don't have a "happily ever after", we can still find satisfaction in their meaningful endings.