It's difficult to say what the theme of Hamlet is from the first scene. We're being introduced to a lot of people and getting the basic situation explained to us, so there's not a whole lot of time for developing the ideas and ideals the play is trying to convey. However, I think one clear emerging idea is when one's kindred are wronged, one has a responsibility to avenge them-- basically the concept of revenge. Shakespeare has set up the perfect situation to make Hamlet mad, not only did his uncle just take over the throne and the kingdom, but he also married his mom (really fast) and is trying to act all fathery to Hamlet. (The whole scene with the King and Queen trying to make Hamlet get over his grief makes me think of a blended family and a step-dad trying to take over the father's position while the angsty teen boy ignores and spurns him.) Then, to top it off, Hamlet finds out his uncle intended for all this to happen; the king murdered his father.

The theme seems to clearly emerge as Hamlet and the Ghost talk-- the ghost immediately urges Hamlet to get revenge on Hamlet's uncle, and even when the Ghost leaves, Hamlet clearly thinks he needs to avenge the ghost.

To answer the questions what is x, etc, I'll just call the theme "revenge" although it is more specific to family and such. What is revenge? It's the idea of punishing someone who has somehow wronged you, often by doing something similar to them. The need for revenge is brought on by feelings of anger, bitterness, and perceived injustice. And the goal in getting revenge is to make yourself feel better (or honor the memory of another wronged person) through the suffering of another.

What does X do? I think the idea of someone getting revenge entertains the audience because revenge is closely tied with the notion of justice. Most people have experienced anger and felt wronged, and would love to see someone get their comeuppance, (often on a smaller scale than life and death). The audience can sympathize with Hamlet for all the wrongs he and his father have suffered and root for him as he attempts to take down the villain. The idea of a revenge plot establishes a clear good guy and bad guy for the audience to cheer for or against.

What does x mean (what will it mean as the action progresses?) I think as the action progresses, Hamlet is going to have very clear cut goals of how to avenge his father (e.g. kill his uncle and make his mom feel bad) and very clear opportunities to do that. However, I think he'll have difficulty making this happen because we've discussed how indecisive he is, so his duty to avenge his father may be neglected. Hamlet may run into opposition, people who believe that he should let go of the past and not attempt to bring justice about by his own means. It's already obvious that he can't go to his mom about this, cause she'd side with his uncle.

As a side note, I'm wondering how old Hammy's supposed to be. He's obviously old enough to know what's going on in a lot of situations, so why didn't he just inherit the throne when the King died?