Hamlet has just recently confirmed that Claudius did in fact kill King Hamlet, so he is very much ready to act -- and kill Claudius in order to avenge his father's death. The problem is, Hamlet is observing Claudius in what he thinks is a moment of prayer. We know that Claudius can't give up what he has gained through his crimes, but Hamlet doesn't.
Hamlet declines to act because he thinks that if he kills Claudius in a moment of prayer, then Claudius's sins will have been forgiven and he could go straight to heaven. That doesn't seem like "good justice" for a killer -- especially in light of the fact that his own father is in purgatory because Claudius killed him while he still had sins on his soul that he must now "burn and purge away" until his soul is fit for heaven.
Hamlet then decides to wait until a better moment to kill Claudius. He thinks maybe he can find Claudius in a sinful act like drunk, or raging, or gaming, or swearing, or some other act "that has no relish of salavation in't." He hopes to kill Claudius and have him go straight to hell -- his comment that he wants Claudius's soul to go to hell as his heels kick at heaven is actually a kind of funny image!
Well, it seems that I don't understand the soliloquy that ends Act 2 either. The word "catch" seems to mean that Hamlet will gain certain knowledge regarding the murder. In the Act 2, scene 2 speech he says: "I have heard / That guilty creatures sitting at a play / Have by the very cunning of the scene / Been struck so to the soul that presently / They have proclaimed their malefactions;"(2.2.577-581 or so). The King does not proclaim a malefaction to any character, only to the audience. So, one might say that Hamlet catches part of the conscience of the King, leaving the most important part unknown.
Speaking as an amateur Shaxberd fan, I'm not sure what he is saying either. On the other hand, I think people read poetry, in part, because the poet puts things in such a way that changing the words changes the meaning. One might characterize the speech as a fantastical or extravagant convergence of thought and passion. Regarding the dialogue immediately after the play within the play, the editors of the new Arden edition note: "Horatio seems to evince some degree of scepticism about the scale of Hamlet's success." One might argue that Hamlet himself is still uncertain as he does use terms in keeping with wagering: "I'll take the Ghost's word for a thousand pound" (3.2.270). The play succeeds, I think, only in the purpose stated in an earlier soliloquy: "The play's the thing / Wherein I'll catch the conscience of the King"(2.2.594). We learn the truth about the murder in a soliloquy from Claudius immediately before Hamlet speaks the speech in question. Hamlet is concentrating on what he will say to his mother as shown in the soliloquy that begins: ""Tis now the very witching time of night"(3.2.371-382). At any rate, Hamlet has a lot on his mind.