Hamlet's soliloquy is important for a number of reasons.
Firstly, he made a pledge to his father's ghost to act swiftly to avenge his father's murder. In the soliloquy, Hamlet expresses anger at himself for not having yet done anything. He compares himself to one of the visiting actors who, in acting out a scene, expresses emotion in a profound way, causing the audience to feel what he feels even though he has no real reason to do so. In contrast, Hamlet cannot do the same—even though he has all the reasons in the world to do so. The contrast makes it clear that Hamlet believes himself a coward. He asks a number of rhetorical questions in this instance:
Am I a coward? Who calls me villain? breaks my pate across? Plucks off my beard, and blows it in my face? Tweaks me by the nose? gives me the lie i' the throat, As deep as to the lungs? who does me this?
Hamlet states that if anyone should do these things to mock or humiliate him for his intransigence and his weakness, he should not feel offended, for the only reason they would do so is because he has less courage than a harmless pigeon.
Secondly, the soliloquy clearly displays Hamlet's self-knowledge and self-loathing. This introspection makes him realize some bitter truths about himself, such as that he does not have the gall to proceed in his revenge. He metaphorically compares himself to an ass, a fool. He uses sarcasm by mentioning that it is indeed “brave” of him; when driven by heaven and hell to commit his vengeance, he is only able to act by expressing his emotions through words and not deeds. He uses similes by comparing himself to a whore and a worthless, swearing kitchen maid in this regard.
Prompted to my revenge by heaven and hell, Must, like a whore, unpack my heart with words, And fall a-cursing, like a very drab, A scullion!
Thirdly, Hamlet in this monologue clearly shows his utter contempt and disdain for his uncle, Claudius. He cries out passionately:
I should have fatted all the region kitesWith this slave's offal: bloody, bawdy villain!Remorseless, treacherous, lecherous, kindless villain….
Hamlet uses powerful metaphors and adjectives to express his intense disgust. Claudius is the same as the entrails of a slave, a man without morals, remorse, or kindness. He now truly realizes just how much he abhors Claudius.
Fourth, it is during this speech that Hamlet finally decides to actually do something to honor the pledge he made to his father's ghost. He now decides that he will use a play to determine Claudius's guilt in his father's murder. He will have the actors enact a scene similar to his father's foul murder. He will then carefully watch Claudius's reaction. If Claudius should act in a guilty manner, Hamlet will then know exactly what to do. It is interesting that Hamlet uses such a careful, indirect method to determine Claudius's guilt; moments earlier, he expressed reckless determination to punish Claudius.
Finally, Hamlet's monologue reveals that he does not entirely trust the ghost. He declares:
The spirit that I have seen May be the devil: and the devil hath power To assume a pleasing shape; yea, and perhaps Out of my weakness and my melancholy, As he is very potent with such spirits, Abuses me to damn me….
Hamlet believes that the ghost might just be a devil who has taken on the guise of his father in an attempt to use his emotional condition and his frailty to do evil, leading him on a path to damnation. Hamlet believes that he needs better grounds to take action. He declares that in this regard, the play will be a better guarantee in proving Claudius's guilt.
...the play's the thing Wherein I'll catch the conscience of the king.