In his soliloquy, Claudius claims to be remorseful for what he has done. But he believes that he cannot really be forgiven for what he acknowledges is a "rank" crime. The reason for this is that he gained much from the crime, including a kingdom and a wife, and he is still in possession of those things. So he is, as he sees it, trapped in his sin. He cannoth get rid of Gertrude, and he certainly cannot step down from the throne. So he remains surrounded by "those effects for which I did the murder," and he concludes that all he can do is pray for forgiveness. This is the moment, of course, when Hamlet is observing him, and fatefully decides not to murder him, for fear that he will go to heaven if he is killed while praying. Claudius, meanwhile, concludes his prayer by lamenting:
My words fly up, my thoughts remain below.
Words without thoughts never to heaven go.
His penitence is insincere, because, in the end, he will not be willing to give up the things that accrued to him as a result of his sin.