Throughout this soliloquy, Hamlet wonders why he can't fulfill his oath to his father and why it would be so hard to avenge the death of a King. He is conflicted here, as can be seen by his self-depreciated remarks like, "I am pigeon-livered" (577) or "Why, what an as am I!" (582).
He is constantly at odds with himself for his unexplained cowardice. Hamlet curses this cowardice often with the same fervor that he attacks Claudius with.
Perhaps another reason why this soliloquy is important is because of it's resolution. Throughout it, Hamlet bullies himself and Claudius, whom he refers to as a "bloody bawdy villain" (580). However, this name calling is what Hamlet needs to get himself worked up. Just as a coach give his team a pep-talk before a big game, Hamlet's uses this strategy to motivate himself into action. It is also influential to note that Hamlet was contemplating suicide in his earlier soliloquies. Although he no longer seems to be, that side of him has not completely dissapated in the audience's mind. This is why he need such a strategy of motivation because not too long ago he was an apathetic, mopey man who saw no use in living. Yet once, he is motivated, we begin to see the change in him. He concludes this soliloquie by saying that "the play's the thing/wherein I'll catch the conscience of the King" (604). Even at this point, after rilling himself up, he is still acting rational and calucuating in his need for definiet proof.
Hamlet's soliloquy in Act IV is in direct contrast to his former thoughts. He voices these new opinions after he is ordered to go to England and encounters Prince Fortinbras along the way. Similar to the previous soliloquy, because once again Hamlet's interaction with with other's forces his passionate nature out. After seeing Prince Fortinbras willing to sacrifice hundreds of men's lives for a single plot of land, something within Hamlet awakens.
