As a child, Jesus was brought by Joseph and Mary to the House of the Lord. This was an act of dedication and recognition that He really belonged to God. Throughout His ministry, people brought children to Jesus and He placed His hands on each of them, and blessed them.

Christians are to recognize everything we have belongs to God (Psalm 127:3-5). The children that are born into our homes belong to Him as well. This dedication is not the salvation of the child, but a public expression and declaration of the fact that they do belong to God, as well as a public declaration by the parents they will seek to do everything in their power, as God gives them wisdom, to see that the child grows up to respect and honor God, and to love and serve Jesus Christ as their Savior. The dedication is more than a ritual. It is a commitment of parents to honor the will and Word of God.

Teachings In Scriptures for Baby Dedications

Jesus Christ's Example: 

"When the time of their purification according to the Law of Moses had been completed, Joseph & Mary took him to Jerusalem to present him to the Lord." 

Luke 2:22

Jesus Christ's Teaching:

 "People were bringing these little children to Jesus to have him touch them, but the disciples rebuked them. When Jesus saw this, he was indignant. He said to them, "Let the little children come to me, and do not hinder them for the kingdom of God belongs to such as these. I tell you the truth anyone who will not receive the kingdom of God like a little child will never enter it." And he took the children in his arms, put his hands on them and blessed them." 

Mark 10:13-16

The Example of Hannah and Samuel: 

"In bitterness of soul Hannah wept much and prayed to the Lord. And she made a vow, saying, "O Lord Almighty, if you will only look upon your servant's misery and remember me, and not forget your servant but give her a son, then I will give him to the Lord for all the days of his life." 

I Samuel 1:10-11

"As surely as you live, my Lord, I am the woman who stood here beside you praying to the Lord. I prayed for this child, and the Lord has granted me what I asked of him, so now I give him to the Lord. For his whole life he will be given over to the Lord."

I Samuel 1:26-28

The Responsibility of Godly Parents: 

"These commandments that I give you today are to be upon your hearts. Impress them on your children." Talk about them when you sit at home, and when you walk along the road, when you lie down, and when you get up!" Deuteronomy 6:6-7

"Fathers, do not exasperate your children; instead, bring them up in the training and instruction of the Lord." Ephesians 6:1-4

Source: www.occ.org