"being confident of this very thing, that he who began a good work in you will perfect it until the day of Jesus Christ:" (ASV)
A lot of people expect when they become Christians that they won't have to worry about sin anymore, then give up when they find that it's not that simple. People who are not Christians often look at the sins of those who are and see it as hypocrisy. While salvation through the blood of Christ does certainly wipe out our sins in God's eyes, it doesn't mean we're all suddenly perfect here on earth. God's not done with us yet.
Once God has a hold on us, we are called to "sin no more" as Jesus said to the woman accused of adultery. (see John 8:2-11 for the whole story) This is not something we can do immediately though. It's a process that will take a lifetime to complete.
In Romans 7, Paul wrestles with this very concept. In his former life, Paul was a man of the law. Until his conversion on the road to Damascus, Paul had been an ardent persecutor of the early church. In fact, the first account we have of him in scripture is his appearance at the stoning of the first Christian martyr. It is clear that Paul had a very good grip on what sin is and isn't under Jewish law.
Yet in his letter to the Romans, Paul notes that he is still struggling against sin. "For the good which I would I do not: but the evil which I would not, that I practice." (Romans 7:19 ASV) He goes on to explain this dichotomy: "But if what I would not, that I do, it is no more I that do it, but sin which dwelleth in me." (Romans 7:20 ASV)
You see, even though we have been saved and our sins washed away in the eyes of God, we still dwell here on earth in bodies that are tainted by sin. But if we read further into Romans, Paul also gives us this advice "For ye received not the spirit of bondage again unto fear; but ye received the spirit of adoption, whereby we cry, Abba, Father." (Romans 8:15 ASV) We don't need to fear punishment for the things our sinful bodies do because Christ has already received the punishment on our behalf. Instead we need to cry out to God, our Heavenly Father, to teach and instruct us, as we are now heirs to His kingdom.
So don't be disheartened if sin seems impossible to overcome. Sin is merely a result of living in a fallen world. God does not abandon us because we sin, rather he constantly is working toward our perfection, so that we can one day dwell in His presence eternally.