For the people of the OT, the principals of old testament laws that God laid out was given as direction in keeping a relationship with God. When we look at the laws of the OT today, we can see that many of the laws that were outlined do not apply to us today, however, the principle of the law does.
The people in the OT did not have the Holy Spirit to guide them into the truth or teach them between right and wrong. A person in the OT knew that if they sinned against God, there would be an action required as atonement for their sin. More often than not, this would be in the form of animal sacrifice.
For anyone who does not yet know Jesus as their Lord and Saviour, they are separated from God. Since Jesus died on the cross and rose again, this meant that man no longer had to be separate from God nor did man have to make sacrifices as a way of atonement because Jesus became the ultimate sacrifice.
God knew that man would not be able to keep his laws; however, by setting out laws, this meant that man would know when he had done something that was wrong. If no law existed, then how would man know when he had committed a sin against God?
Since Jesus died on the cross and rose again, when someone gives their life to Christ, we are also given the Holy Spirit. It is now the Holy Spirit who convicts us when we have done wrong; therefore, many of the laws that were set out in the OT are no longer necessary for us to comply with when we have sinned.
For someone who wants to have a close relationship with God, if we do something wrong, even though sometimes we may not fully understand what we did wrong, we would notice our relationship with God is different or there seems to be something separating us from enjoying the fullness of our relationship with Him, in this case, this is where the Holy Spirit can show us what is wrong and what needs to be done in order for us to enter back into that fullness of our relationship with God.
We no longer have to go and kill an animal to get ourselves right with God, we instead have to recognise what we did, come before God and repent and ask for forgiveness, and if we do this in our hearts, Jesus will forgive us and we can continue on pressing in with God.
Even though we no longer have to make animal sacrifices as a way to atone for sin, the principle is still the same. There was sin that occurred and separated us from God, or put a spanner in our relationship with Jesus, so we needed to recognise that sin and ask for forgiveness.
Since the sin of Adam and Eve in the Garden of Eden, all men were separated from God, because of what Jesus did on the cross and through His resurrection; this meant that man could once again have a close and personal relationship with God. Before Jesus, man knew God in a different way; God lived in temples or tents, now, God lives in the hearts of those who accept Jesus into their lives as Lord and Saviour.
For us today, to maintain a relationship with God, we have the Holy Spirit to help lead and guide us into walking in righteousness, and to restore a relationship with God, we need to repent from sin when we have done something wrong.
You could say, Jesus could not have made it any easier for us to have a right relationship with Him. Sin made it difficult in the times of the Old Testament, but since the Resurrection of Jesus, He made it so we no longer had to make sacrifices in order to have a righteous relationship with God, we just have to learn to walk in His ways by the help of the Holy Spirit and ask for forgiveness when we mess up.