To be dedicated is to be set apart, to be committed and devoted to a cause, ideal or purpose. For a Christian parent to bring their child before the church and dedicate their child to God they are committing themselves to bringing up their child in a Godly way. They are setting their child apart for the Kingdom of God. And they are continuing a tradition that dates back to the first Jewish passover.
When the children of Israel were being delivered from slavery in Egypt, the final plague, the angel of death, was sent to kill the firstborn male, both man and beast, throughout the Egyptian as well as the Jewish households. Anyone could be saved from this death by applying the blood of a lamb to the doorposts of their house. And because the angel of death passed over and firstborn was saved, God instructed the people that henceforth the firstborn would be sacred, set apart, and holy unto the Lord God. (Exodus 13:1-15). The firstborn animals were themselves to be sacrificed, and God made provision for a substitute sacrifice for the firstborn child.
When Jesus himself was born, as was the custom, his parents took him to Jerusalem to offer a sacrifice on his behalf, as an offering, a substitution for his life. (Luke 2:22-24). The word says they brought him to Jerusalem to present him to the Lord.
Christian parents see children as a blessing from God and want to thank God and dedicate themselves to raising up their children according to God’s ways. So they bring their children to the church for a dedication ceremony, just as Jesus’ parents brought him to the temple. They dedicate themselves to raising the child in the nurture and admonition of the Lord, so that the child becomes a Godly man or woman for the Kingdom of God.
The Old Testament tells the story of a mother who prayed and prayed to God for a child, but was unable to have one for years. When God finally blessed her with her first child she promised to dedicate this child to the Lord. He was the prophet Samuel, and from the time the child was weaned, his mother Hannah literally gave him to the high priest to serve and work in the temple for God.
In the dedication ceremony Christian parents symbolically give the child up to God, often literally handing the child over to the minister. Having prayed over the child and blessed the child the minister gives the child back, symbolizing that having given the child up to God, God now gives the child back to them to raise.
The parents are making a public proclamation that they will live their lives for God and commit themselves to being Godly parents and examples of Kingdom living for their children. Children are a blessing from God, and like all things God gives us, He expects us to be good stewards. When we as parents understand our children belong to God and He has entrusted them to us, it should change the way we parent.