way he can ever fully repay him.

Macbeth then answers by stating that it is his duty to the king and the state, as well as the king's children and servants, to do what he can to serve them without expecting any other reward. He says, too, that doing his duty is its own reward.

Duncan responds that making Macbeth thane of Cawdor is only the first part in a glorious career he has mapped out for his loyal servant. Duncan, carried away by enthusiasm, completely misses the wooden and cliched quality of Macbeth's speech to him on duty.

Macbeth may on some level be saying what he believes to be true—that a subject should serve his king selflessly—but we know his mind is running along other paths, carried away by the witches' prophesy. Macbeth at this juncture seems to be expressing what a loyal subject should be but also trying to make sure that Duncan has no reason to suspect that he might be already plotting to take matters into his own hands to become the new monarch.

It's act 1, scene 4 in Macbeth, and King Duncan's enemies have been comprehensively vanquished on the field of battle. This is due in no small part to the exemplary courage and military skill of Macbeth. Duncan is very grateful for Macbeth's valiant exploits and has rewarded him with the title of Thane of Cawdor. Despite his generosity, Duncan tells Macbeth that he was feeling a little guilty for not having thanked him enough:

O worthiest cousin, The sin of my ingratitude even now Was heavy on me. Thou art so far before That swiftest wing of recompense is slow To overtake thee. Would thou hadst less deserved, That the proportion both of thanks and payment Might have been mine! Only I have left to say, More is thy due than more than all can pay.

Macbeth replies that he needs no honors bestowed upon him; loyal service to the king is its own reward. This is no false modesty on the part of Macbeth; at this stage of the play, he isn't seriously contemplating Duncan's assassination. Nevertheless, the Weird Sisters have already planted the seeds of ambition in his overactive imagination. They prophesied that he would be Thane of Cawdor, and that's precisely what he's become. It's notable too that the former Thane of Cawdor was a traitor who betrayed his king, and this has cost him his life. The previous thane's fate eerily foreshadows Macbeth's own treachery and eventual demise.

To put this quote into context, King Duncan has just expressed his gratitude to Macbeth for performing so well on the battlefield and bringing to an end the rebellion of Macdonwald. This quote is a response to Duncan's gratitude and is spoken by Macbeth.

In terms of its literal meaning, Macbeth is saying that having the chance to serve King Duncan is all the reward he needs. Moreover, Macbeth believes that Duncan does not need to thank him for what he did in battle. In fact, Duncan's job is to accept Macbeth's service and loyalty since it is what Macbeth owes to him. Finally, Macbeth compares his relationship with Duncan to the relationship between a child and his parent. In his mind, serving Duncan is as natural and right as a son serving his father.

Looking deeper, this quote portrays Macbeth as the perfect Thane. Not only he is completely loyal and subservient, he expresses total gratitude to Duncan for being such a great king.

But we have to wonder just how sincere this quote really is. In the previous scene, Macbeth heard the witches prophecies and immediately began thinking about murdering Duncan so that he can take the throne for himself. Either Macbeth still feels some loyalty toward Duncan or he is trying to ensure that nobody suspects him of committing Duncan's impending murder.

King Duncan has bestowed upon Macbeth the title Thane of Cawdor, in addition to the title he already has, as a reward for his bravery and loyal service to the crown during the battles against the rebel Macdonwald and the Norwegian king.  Macbeth was already the Thane of Glamis, and now he is Thane of Cawdor as well. 

When Macbeth arrives and sees Duncan, he greets Duncan as his friend, kinsman, and king.  Duncan expresses his gratitude to Macbeth for everything that he has done to protect Scotland, and Duncan says that he feels as though he cannot actually reward Macbeth enough for all his service.  Macbeth responds with the lines you cite, saying, 

"The service and the loyalty I owe,

In doing it, pays itself. Your highness' part

Is to receive our duties: and our duties

Are to your throne and state, children and servants."

What he means is that it is his duty to serve the crown, and this service is its own reward.  It is the king's job simply to receive the services his subjects provide because it is their duty.  Finally, he says that these duties performed by his subjects are owed to Duncan the way children owe their parents and servants owe their masters.