One of the great things about this play is that it shows us about governance and power. To state the theme quite simply, it is, Power corrupts and absolute power corrupts absolutely.
Consider what happens. At the beginning of the play, we meet Macbeth, the protagonist and tragic hero of the play. He is a good man it would seem. A valiant warrior. A loyal Scotsman.
Is he ambitious? Of course he is. This was not a time in Scottish history where the son necessarily followed his father onto the throne. With constant threats from the raiding Norsemen, a boy king would not have been a good thing. You needed a strong and proved military leader on the throne. Does Macbeth, at the beginning of the play fit the bill? Yes. Does Malcolm? No. he has not proved himself in battle. In fact, he had to be rescued...by Macbeth.
The prophsey that he will be king in the future seems thwarted by Duncan naming his son, Malcolm as his successor. Does Macbeth feel cheated? Yes.
Does Lady Macbeth feel that her husband rather than a seemly weak and untested youth (Malcolm) deserves to be king? Yes.
The combination of Macbeth's ambition, the weird sister's prediction, and the urging of Lady Macbeth all combine to lead Macbeth from hero to tyrant.
Once he murders Duncan. he must continue to murder to cover up his actions. We hear how Scotland has become a horrible place to live. Fear and distrust are the norm under Macbeth. Neighbor spys on neighbor. People don't know who they can trust. He does not use his power wisely or for the good of his subjects. He uses his power to control and punish those who don't fall in line. Look what happens to the Macduff family.
In the play The Best Man, the old and dying former president tells one of the candidates, "Power is not a toy we give to good children. It is a weapon and the strong man takes it and he uses it."
Shakespeare shows us this terrible lesson in Macbeth. He uses his power to beat his people over the head. One of the great lessons of history is the corrupting nature of power. Once Macbeth killed Duncan he was corrupted by power.
Macbeth is a Tragedy, and as such, requires (according to Aristotle's definition) a Tragic Hero to fall prey to his tragic flaw, which instigates the Hero's downfall, ending in his undoing. The character of Macbeth is this Tragic Hero, and as mentioned in the previous answer, it is his ambition that proves to be his tragic flaw, the instigator of his undoing.
However, Shakespeare takes this classic structure of Tragedy and changes it up a bit. Not only is ambition Macbeth's flaw, he is aware of it from even before the murder of Duncan. This self-awareness is expressed when he is onstage alone with audience in Act I, scene vii. In this speech, he admits that killing Duncan will not make him King in any "free and clear" way, but simply bring on new problems, not the least of which is the suspicion that it will stir up in those around him. And yet he proceeds, because of his "vaulting ambition."
In this moment, Shakespeare takes a dramatic step away from the classic Tragic structure, by having Macbeth confess his weakness to the audience, proceeding with the course of action that he himself suggests might lead to his own downfall. Shakespeare, in showing Macbeth's self-awareness, not only offers the audience the opportunity to experience "fear and pity" at Macbeth's demise, but also to become aware of the potential for this very human course of action in their own selves.
And so, the audience can actually identify with Macbeth, something that the classic structure of Tragedy wasn't really designed to do. Today, we still look, as audience, to identify with characters in this way.
Macbeth is the protagonist in the play and the course of events follows his personal journey as he deals with his ambition. After hearing the witches' prophecy, Macbeth's sense of morality becomes challenged by his desire and ambition--he desperately wants to be king, but he is unsure of how he should secure this fate. At first, he resolves to let "Chance" work in his favor as he waits for the natural order of things to come about. However, he is persuaded by Lady Macbeth to be strong and take matters into his own hands. Macbeth eventually agrees with his wife, but he feels very guilty after murdering King Duncan. But once this is done, Macbeth continues to let his ambition take over him and he does ill deeds to cover up his crimes and maintain his position as king. In the end, Macbeth knows that nothing good has come of his actions, but he still fights to the death in support of (or maybe to atone for) what he has done throughout the play.
I think Macbeth's role in the play Macbeth has contemporary relevance.
Macbeth became a victim of inordinate ambition. He bartered his scrupules and conscience for his lust for power. Before killing Duncan he hesitated as his conscience pricked. Later he beacme a seasoned criminal. He felt little qualms in killing lady Macduff and her innocent children.
To consolidate his position, Macbeth sacrificed everything- his sleep and his sweet relation with his wife. In the end he became a loner. After the sudden demise of Lady Macbeth, he realised the futility of all his frenzied actons beautifully illustrated in the lines:
"Life is full of sound and fury
In today's fast track life there is a Macbeth everywhere. Like unbridled horse people are madly running after money and power little realising their moral bankruptcy is taking them to the abyss of depravity.
In modern sense Macbeth's role is that of an eye-opener to all young aspirants. There is nothing wrong in being ambitious. But pursuing foul means to accomplish one's dream is suicidal.
So dear readers, Macbeth by his tragic fall tells us to soar high but with patience and perseverance.