Ghosts, perverse family drama, and a vow of revenge: Hamlet is all geared up to be a traditional bloody revenge play… and then it grinds abruptly to a halt. The play isn't about Hamlet's ultimately successful vengeance for his father's murder at all—that's taken care of in about two seconds during Act 5. Instead, most of the play is concerned with Hamlet's inner struggle to take action. Our point? The play is a lot more interested in calling into question the validity and usefulness of revenge than in satisfying the audience's bloodlust—although, sure, it does that too. Shakespeare had a theater to fill, after all.
In this way, this speech connects many of the play’s main themes, including the idea of suicide and death, the difficulty of knowing the truth in a spiritually ambiguous universe, and the connection between thought and action. In addition to its crucial thematic content, this speech is important for what it reveals about the quality of Hamlet’s mind. His deeply passionate nature is complemented by a relentlessly logical intellect, which works furiously to find a solution to his misery. He has turned to religion and found it inadequate to help him either kill himself or resolve to kill Claudius. Here, he turns to a logical philosophical inquiry and finds it equally frustrating.