Question: "What is baby dedication? Is child / baby dedication biblical?"
Answer: In the majority of Protestant denominations that practice it, child dedication is a symbolic ceremony undertaken by Christian parents soon after the birth of a child. Some churches perform these ceremonies en masse and have several couples and children participating at the same time. The rite is intended to be a public statement by the parents that they will train their children in the Christian faith and seek to instill that faith in them. The congregation often responds through responsive reading or some other method to affirm that they, as a church family, will also seek to encourage the parents to bring up the child in the faith. There is no implied salvation in the ceremony, and it varies from church to church.
The idea of dedicating a child to the Lord can certainly be found in the Bible. Hannah was a barren wife who promised to dedicate her child to God if He would give her a son (1 Samuel 1:11). Luke 2:22 begins the account of Mary and Joseph taking Jesus to the temple after forty days in order to dedicate Him to the Lord. This was slightly more involved since it involved a sacrifice, but once again this ceremony did not indicate any level of salvation.
Child / baby dedication is not one of the two ordinances—baptism and the Lord’s Supper—required of Christians in the New Testament. As Christians, we are baptized and participate in the Lord’s Supper as outward and public signs of what Christ has done within us. While baby dedication is not an officially instituted ordinance of the church, there does not seem to be any conflict with Scripture as long as parents do not view it as assuring the salvation of the child.