First, a summary of Act Two of Hamlet:
The act starts out with Polonius talking about his son, Laertes, who has returned to France. He discusses how he wants to know more about how his son is behaving and sends a spy. Ophelia then enters telling how Hamlet is wild. Next, Claudius seeks out the reason behind Hamlet's strange behavior. Polonius claims to understand Hamlet's behavior and states it is due to his love for Ophelia. Polonius and Claudius decide to spy on Hamlet. Hamlet enters and has many discussions about love, the coming play, and then he delivers some of his greatest lines, musing on his father's ghost and deciding to stage a play that is about the murder of his father. He believes this will show if the king is guilty of the murder.
This act is essentially devoted to the "madness" of Hamlet. While subplots are discussed, most of the characters are curious about the source of Hamlet's strange behavior. Hamlet is also concerned with his feelings, but we are not able to see Hamlet's behavior until we have heard about it from all the other characters. This allows insight into the other characters, as well as the overall mood around Hamlet.
Compared to the rest of the play, the tone of this act is somewhat light. There is a lot of talking about Hamlet's madness, but there are no significant deaths or active events. Everyone is thinking about Hamlet, and there is a lot of confusion, but this act is largely setting up the actions that will occur later in the play.