The Thane of Cawdor was found guilty of conspiring with the Norwegian side against king Duncan. Although he had plotted with Macdonwald to overthrow Duncan, the Norwegians were eventually defeated. This is proclaimed by the sergeant, who informs Duncan of the outcome of the battle, and he says that Macbeth was the one who fought valiantly and who helped king Duncan's side emerge victorious from the battle:
For brave Macbeth--well he deserves that name--
Disdaining fortune, with his brandish'd steel,
Which smoked with bloody execution,
Like valour's minion carved out his passage
Till he faced the slave;
Which ne'er shook hands, nor bade farewell to him,
Till he unseam'd him from the nave to the chaps,
And fix'd his head upon our battlements.
Ecstatic upon hearing the news, king Duncan orders that the old Thane of Cawdor be executed:
No more that thane of Cawdor shall deceive
Our bosom interest: go pronounce his present death,
And with his former title greet Macbeth.
He also orders that his title be given to Macbeth, and he calls Macbeth "valiant cousin" and "worthy gentleman." What is unfortunate for Duncan is that he will be betrayed by Macbeth in the same way he was betrayed by the old Thane of Cawdor. Macbeth will conspire to murder Duncan in order to fulfill his own ambitions, even though King Duncan is his kinsman and his leader.
In Act I, Scene 2, of Macbeth, a captain of Duncan's army reports to his king that he has been wounded fighting the Irish, but Duncan's generals, Macbeth and Banquo, have fought with much valor and violence, especially Macbeth, who cut Macdonwald from bottom to top. Then, a Scottish nobleman enters to inform King Duncan that the Thane of Cawdor has been defeated in his treachery along with the army of Norway with whom Cawdor has conspired. Hearing of Macbeth's raw bravery, King Duncan orders that the hero Macbeth be given Cawdor's title, and Ross is sent to deliver the news to Macbeth.
Then, in Act I, Scene 4, Malcolm, Duncan's son who has been made Prince of Cumberland, reports to his father the king that the execution was carried out on the thane of Cawdor. Malcolm says that he received a report that Cawdor confessed his treasons, before dying,
Implored your Highness' pardon and set forth
A deep repentance: nothing in his life
Became him like the leaving it. He died
As one that had been studied in his death,
To throw away the dearest thing he owed
As twere a careless trifle. (1.4.6-11)
King Duncan sadly reflects that he had not known the type of man Cawdor has been. For, he has thought the Thane of Cawdor a thoughtful man.
He was found a traitor to the King of Scotland. He had helped the Norway and was caught. Because he was disloyal, he was executed. Because Macbeth showed such valiant efforts with great results in battle, he earned the new title as Thane of Cawdor to take the other's place. What is interesting is that he becomes just as disloyal to the king--even worse--after he receives that same title--because he kills the king. Here is where Ross explains to the king how Cawdor was unfaithful.
He was definitely executed because of treasonbut most importantly to make way for Macbeth as it was destined