Claudius' soliloquy about his remorse over his murder of Hamlet's father is important to the play because it's the one place where we learn how Claudius feels about what he has done. The rest of the play is all about how Hamlet feels about what Claudius has done, and I think it rounds out the play to get it from a different perspective.

From the soliloquy I can see that Claudius feels sorry for the murder, but not sorry enough. He says, "Oh, my offense is rank, it smells to heaven." He wants to pray for forgiveness of his offense, but laments, "Pray can I not," because "I am still possessed of those effects for which I did the murder - My crown, mine own ambition, and my queen." He murdered Hamlet's father in order to get those things and he is not willing to give them up. He realizes that true repentance would be willing to give then up, and therefore, he is not really repentant. This is why at the end of his prayer, he says "Words without thoughts never to heaven go." There's no point in saying he is sorry because God knows he doesn't really mean it. So, the best he can do is pray that God will make him sorry, by pleading, "Heart with strings of steel, be as soft as the sinews of a new-born babe."

All of this shows that Claudius is introspective and honest with himself. It also does contradictory things to my opinion of him. Depending on how I look at it, this prayer can make me feel sympathetic towards Claudius as I learn about the inner torture he is going through and how awful he feels about killing Hamlet's father. On the other hand, it also makes me more