Jesus said, "Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill." (Matt 5:17) Many Christians understand the first part of that statement, but ignore the second. What does it mean that Christ came to fulfill the law? Paul tells us in Rom 8:3-4;

"For what the Law could not do, weak as it was through the flesh , God did: sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh, so that the requirement of the Law might be fulfilled in us, who do not walk according to the flesh but according to the Spirit."

That means that the law is unable to save or justify anyone, because we are weak and sinful. But Christ has fulfilled the righteousness of the law for all who put their faith in Him. Paul also makes it clear that the purpose of the law is not to justify, but to bring the awareness of sin:

"..because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin. But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets, even the  righteousness of God through faith in Jesus Christ for all those who believe." (Rom 3:20-22)

This is not to say that as Christians we don't care about God's law. We want to please Him in all things, now more than ever, so we walk carefully to obey Him, but we also know that we stumble often and fail at times. Those failures have been taken away by the sacrifice of Jesus, and believers will not come into judgment (John 5:24).