What does Sophocles' Antigone communicate to the audience?

In addition to the classic issue of hubris, or excessive and unrelenting pride, which is a perennial one in Greek tragedy, Antigone poses two related questions about the nature of citizenship and political power.
First, the dilemma posed to Antigone revolves around the perspective of the citizen or subject: is every decree of a ruler to be obeyed, or are there duties that may be more important than civic statutes? Antigone is never in doubt about the answer, even in her opening dialogue with Ismene:

IsmeneYou plan to bury him—when it is forbidden to the city?
AntigoneYes, he is my brother, and yours too, even if you wish it otherwise. I will never be convicted of betraying him.
IsmeneHard girl! Even when Creon has forbidden it?
AntigoneNo, he has no right to keep me from my own. (44-48)

Later, in her confrontation with Creon, she explicitly states than her disobedience to his decree was just,

since it was not Zeus that published me that edict, and since not of that kind are the laws which Justice, who dwells with the gods below, established among men. Nor did I think that your decrees were of such force, that a mortal could override the unwritten and unfailing statutes given us by the gods. (450-455)

Creon's dilemma is from the perspective of the ruler: should he demand obedience, or should he be open to critique and correction from the citizens or subjects? His clearest answer is given when challenged by his own son, Haemon, where Creon begins with a speech in which he states:

whomever the city may appoint, that man must be obeyed in matters small and great and in matters just and unjust...But there is no evil worse than rejection of the ruler (anarchia). (lines 666-667, 672)

The argument between Creon and Haemon leads to this furious stichomythia:

CreonShall the city prescribe to me how I must rule?
HaemonSee, there, how you have spoken so much like a child.
CreonAm I to rule this land by the will of another than myself?
HaemonThat is no city, which belongs to one man.
CreonDoes not the city by tradition belong to the man in power?
HaemonYou would make a fine monarch in a desert. (734-739)

Creon's demand for total and unquestioning obedience in all things turns out to be the truly tragic decision of the play, since his law against the burial of Polyneices brings pollution on the city (line 1015) and the deaths of Antigone and his own son.
The play's answer to both questions, then, is in favor of Antigone and Haemon's view that there are limits to the ruler's power, and that both the citizens and the ruler should recognize this.
An important addendum as to the message of Antigone has to do with the role of women. Creon's demands of obedience are crucially intertwined with his refusal to listen to a woman:

Therefore we must defend those who respect order, and in no way can we let a woman defeat us. It is better to fall from power, if it is fated, by a man's hand, than that we be called weaker than women. (677-680)

This is seen as well in his argument with Haemon, where Creon repeatedly condemns and insults his son for supporting a woman (740, 746, 756).
The fact that the play vindicates Antigone's actions and perspective on political authority and its limits, over against Creon's tyranny and misogyny, lead many to consider Antigone to be a striking, early example of feminist social critique.
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0186%3Acard%3D1

In Antigone, Sophocles communicates the importance of being humble. 
At the end of Antigone, there is a profound sense of emptiness.  We have seen Creon and Antigone collide with one another because they believed in the authenticity of their convictions.  Antigone believed she was doing right by her beliefs.  Creon is equally adamant in his unwillingness to compromise.  Family members appeal to both of them to change their mind.  However, neither one sacrifices their ego and, as a result, the unthinkable takes place.  While Creon does relent, it is too late.  The deaths of Creon's son and wife along with Antigone's death represent sadness resulting from human foolishness. 
Sophocles communicates the danger of self-aggrandizement.  He conveys the calamity that can await when we believe that we are better, smarter, and stronger than we really are.  This is revealed at the drama's conclusion. Creon appears before the Chorus and the audience as a broken man:

Let this rash man be led out of the way,who, my child, unwillingly slew you,and this woman, you, too—alas! I haveno where to turn to, nothing to lean on,for everything goes cross in my hands,and a difficult fate falls on my head.

Creon's language is very different from the bluster he displayed throughout the drama.  He has recognized that living a life without humility has made him a "rash man." He knows that his hubris resulted in the deaths of his son and wife.  He is forced to admit his limitations, a reality he would not previously entertain. Creon communicates how "a difficult fate" crushes us when we do not limit our ego and listen to others' counsel.
Sophocles communicates how we need to live within our limitations in order to find happiness.  In the drama's final lines, the Chorus communicates how we must be different than Creon or Antigone:   

Knowledge truly is by far the most important partof happiness, but one must neglect nothingthat the gods demand.Great words of the over-proudbalanced by great fallstaught us knowledge in our old age.

We are punished through "great falls" when we live as "the over-proud." Sophocles tells the audience that knowledge and wisdom mean living with humility and deference to something larger than ourselves.  Creon and Antigone communicate the dangers of living otherwise.