Shakespeare's attempt to create sympathy for Claudius serves two purposes. First, Shakespeare refers in several of his plays to the two sides that exist in everyone, a person's ability to be good or evil. In showing this repentent guilt in Claudius, Shakespeare acknowledges this existence. Claudius is afraid of God's punishment for his evil deeds, so he attempts to pray one more time, seeking God's salvation for his crime. This makes Claudius more believable as a human being.
This brings us to Shakespeare's second reason for allowing us to see Claudius as a more sympathetic character. Hamlet sees Claudius praying, and Hamlet realizes he must postpone killing Claudius. If he murders him while at prayer, Claudius will go to heaven rather than hell. Hamlet vows to kill him while the king is "about some act/That has no relish of salvation in't--...". What Hamlet doesn't realize is if he had waited for a few seconds, he could have killed Claudius because he still hadn't been able to pray, and Claudius gets up as Hamlet leaves.
Rather than create a work that portrays a simplistic good guy/bad guy scenario, Shakespeare presents this scene where a Claudius is struggling with the effects of his murderous act. It's a very human struggle laced with guilt, fear, and greed. It allows the audience to see the complexity of Claudius' situation/character as well as presenting the themes guilt and the consequences of corrupt actions.