Baby dedication is where the church asks for God's blessing over a child's life and the parents commit to raising them in accordance with scripture.
"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.” - 1 Samuel 1:27-28
Train up a child in the way he should go; even when he is old he will not depart from it. - Proverbs 22:6