It is significant that Claudius admonishes Hamlet as he addresses him for the first time in the play. Claudius is clearly the antagonist, and he begins his hour upon the stage in a blatantly adversarial role. Were Claudius' demeanor not enough to tell the audience that the two are rivals, Hamlet underscores the discomfort of their relationship by asserting his disgust for the man with his own opening statement.
The key words that exemplify the critical purpose of this scene include "show," "seem," and "play." Cornelius and Voltemand say they will "show our duty." Laertes "came to Denmark to show" his allegiance to King Claudius. Gertrude asks Hamlet, in reference to his "nighted color," "Why seems it so particular with thee?" Hamlet responds to her question by using the word "seems" twice in a single sentence, and he says he cannot pretend, but rather, must be what he is. He then goes on to say that the moods and shapes of grief are true for him. Though his emotions may seem to be those of an actor, he is not acting. Everything in this scene points to the challenge of discerning appearance from reality, a challenge that becomes more pronounced when Horatio tells Hamlet about the appearance of the Ghost.
