Act I, Scene 2 of Macbeth takes place at a camp near Forres. There King Duncan and his sons Malcolm and Donaldain along with the nobleman Lennox encounter a bleeding captain. Duncan immediately asks for a report from this captain. The captain describes the battle led by the allied forces of Norway and Ireland, led by the rebel Macdonwald as a desperate one in which
As two spent swimmers that do cling together(10)
And choke their art.
the merciless Macdonwald and Macbeth have battled. Macbeth, himself very brutal, slays Macdonwald by brandishing his sword and "carving out his passage" until he has reached him. Without any courtesy to the rebel, Macbeth brutally slices him from the navel to the jaws. Then, Macbeth places Macdonwald's head on top of the fort's wall.
The Thane of Cawdor is also revealed to have been plotting against Duncan, the king of Scotland; however, whether he has worked alone or with Macdonwald is unknown. The nobleman Ross then describes how the Norweigan army began their assault after Macbeth and his men have defeated Macdonwald. Enraged, rather than fearful, Macbeth and Banquo "redoubled strokes upon the foe," and deafted the opposing forces.
Impressed by Macbeth's bravery, King Duncan orders the death of the traitorous Thane of Cawdor and gives his title to Macbeth, declaring,
What he hath lost, noble Macbeth hath won.
This scene clearly establishes both the bravery of Macbeth as well as his potential for brutality which is later displayed in Macbeth's acts of "vaulting ambition" after he hears the predictions of the three witches.
I agree with the above answer to a point but disagree as to who defeated and captured the Thane of Cawdor. According to Ross, he is defeated by Bellona's bridegroom. Although most footnotes identify Ballona's bridegroom as Macbeth, I contend that it was Macduff.
This battle is reported by Ross, who tells the king that he comes from Fife. Fife is located in the north of Scotland. The Thane of Fife is Macduff who is also Ross's kinsman. If, as many think, that this is a reference to Macbeth, this causes several questions. How did Macbeth get from his battle to Fife? Why would Macduff give over command to an equal thane? Why doesn't Macbeth know that the Thane of Cawdor was a traitor if he defeated and and captured him in the battle?
I contend that Shakespeare was setting up Macbeth and Macduff for the final and ultimate battle between these two warriors. Ross was bragging about his kinsman, Macduff not Macbeth, by comparing him to Ballona's bridegroom. Shakespeare's audiences would have known by the main clue, Fife.
So, why does Ducan give Macbeth the Thane of Cawdor's title and lands? He rescued Malcolm, the prince, so it is his reward.