These lines come after Claudius has been trying to pray after he sees the play "The Mousetrap." What he doesn't know is that Hamlet sees him praying and almost kills him during that time. Hamlet decides not to kill Claudius because, according to Elizabethan belief, a person killed in the middle of prayer and confession of sin would go directly to heaven. Hamlet knows his own father was killed when he was sleeping. His father said the murder meant that he was "sent to my account/With all my imperfections on my head." ( Act I,scene v, lines 83-84)In other words, he is not in heaven, but in purgatory waiting for his sins to be burned away.
So Hamlet decides not to kill Claudius because he wants to wait until Claudius is doing something sinful, then kill him so he will be sent to hell or purgatory. Then Hamlet leaves and Claudius says these lines,"“My words fly up, My thoughts remain below. Words without thoughts never to heaven go” In other words, he is not willing to repent of his sin, therefore, the sin will not be forgiven. So Claudius' words are flying up but because he does not have the repentance to go with the words, his words will never reach heaven. Ironically, Claudius is in an unrepentant state and if Hamlet would have killed him, Claudius would not have been set to heaven, but the hell or purgatory as he wished.