When hands were laid on the Old Covenant animal sacrifices a transfer or impartation took place symbolically. The sins of the offerer were imparted to the animal, causing the animal to carry or bear those sins and suffer the penalty of death for them. That is what actually  happened at Calvary. The Lamb of God became sin on our behalf. Our sins and the penalty for those transgressions were transferred to the innocent One who had never committed or even known sin before that moment.

He made Him who knew no sin to be sin on our behalf, so that we might become the righteousness of God in Him. 2 Corinthians 5:21 (NASB) 

The transfer and carrying of our sins is mentioned in Isaiah 53.

All of us like sheep have gone astray, Each of us has turned to his own way; But the LORD has caused the iniquity of us all To fall on Him. Isaiah 53:6 (NASB) 

As a result of the anguish of His soul, He will see it and be satisfied; By His knowledge the Righteous One, My Servant, will justify the many, As He will bear their iniquities. Isaiah 53:11 (NASB) 

The physical laying on of hands in the Old Covenant was spiritually fulfilled in the New.

The laying on of hands also imparts blessings. Even in the Old Covenant blessings were imparted in this way.

But Joseph was upset when he saw that his father placed his right hand on Ephraim’s head. So Joseph lifted it to move it from Ephraim’s head to Manasseh’s head. 18  “No, my father,” he said. “This one is the firstborn. Put your right hand on his head.” 19  But his father refused. “I know, my son; I know,” he replied. “Manasseh will also become a great people, but his younger brother will become even greater. And his descendants will become a multitude of nations.” 20  So Jacob blessed the boys that day with this blessing: “The people of Israel will use your names when they give a blessing. They will say, ‘May God make you as prosperous as Ephraim and Manasseh.’” In this way, Jacob put Ephraim ahead of Manasseh. Genesis 48:17-20 (NLT) 

In the New, Jesus laid his hands on children to bless them.

One day some parents brought their children to Jesus so he could touch and bless them. But the disciples scolded the parents for bothering him. 14  When Jesus saw what was happening, he was angry with his disciples. He said to them, “Let the children come to me. Don’t stop them! For the Kingdom of God belongs to those who are like these children. 15  I tell you the truth, anyone who doesn’t receive the Kingdom of God like a child will never enter it.” 16  Then he took the children in his arms and placed his hands on their heads and blessed them. Mark 10:13-16 (NLT) 

He laid hands on the sick to heal them and set them free from demons.

Now when the sun was setting, all those who had any who were sick with various diseases brought them to him, and he laid his hands on every one of them and healed them. 41  And demons also came out of many, crying, “You are the Son of God!” But he rebuked them and would not allow them to speak, because they knew that he was the Christ. Luke 4:40-41 (ESV) 

We are instructed to do the same.

And these signs will accompany those who believe: in my name they will cast out demons; they will speak in new tongues; 18  they will pick up serpents with their hands; and if they drink any deadly poison, it will not hurt them; they will lay their hands on the sick, and they will recover.” Mark 16:17-18 (ESV) 

It happened that the father of Publius lay sick with fever and dysentery. And Paul visited him and prayed, and putting his hands on him healed him. Acts 28:8 (ESV) 

The baptism in the Spirit and spiritual gifts are also imparted in this way.

Then they laid their hands on them and they received the Holy Spirit. Acts 8:17 (ESV) 

Do not neglect the spiritual gift within you, which was bestowed on you through prophetic utterance with the laying on of hands by the presbytery. 1 Timothy 4:14 (NASB) 

God often uses physical touch to communicate spiritual blessings.

We are human beings made up of a spirit, soul, and a body. Each part is important. Obviously God can impart spiritually without the laying on of hands, as when he healed from a distance by simply speaking a word. (Matthew 8:5-13) Nevertheless, God in his wisdom uses the laying on of hands to impart blessings. This why it is a good thing to lay hands on people when we pray for them. Sometimes people feel a tangible “touch” of the Spirit when we do that. Why not give it a try?