Claudius says Hamlet is a danger, and orders Rosencrantz and Guildenstern to prepare to leave for England. They agree that if the King were to die it would be a tragedy for the country, and exit.
R and G echo belief that health of a country is tied to the legitimacy of the King. They don't know that Claudius isn't legitimate.
Polonius enters with news: Hamlet is headed to Gertrude's room, where Polonius will hide behind a tapestry.
Polonius is still stuck in the old plot, while new plots are afoot.
Finally alone, Claudius cries out that his "offense is rank!" (3.3.36). He wants to pray, but doesn't see how he can ask forgiveness when he possesses the spoils of the murder, neither of which he wants to give up: Gertrude and the throne. Yet he kneels to pray.
Now audience knows that Claudius both guilty and unable to repent. In other words, he deserves to be killed by Hamlet...
Hamlet enters. He draws his sword to kill Claudius and be revenged. But it occurs to him that if he kills Claudius as Claudius prays, then Claudius will go to heaven. That isn't real revenge, especially when Claudius murdered Hamlet's father before he could pray, sentencing Old Hamlet to torment in purgatory. Hamlet decides to wait until Claudius is sinning to kill him. Hamlet exits.
Why does Hamlet delay again? Because he realizes that Christianity is arbitrary. Getting to heaven is based on when you pray rather than who you are. Religion itself seems to have been duped by appearance. Hamlet waits to get true revenge.
Claudius stops praying. The attempt was useless: "My words fly up, my thoughts remain below. / Words without thoughts never to heaven go" (3.3.97-87).
The ultimate irony. Hamlet is himself duped by appearance: Claudius only looked like he was praying.