Today, these parents have come to claim God's promises to and about their children.
God says to us, "I will be a God to you and to your children." In baptism, we claim that covenant pledge and God acts to make good on that pledge. In baptism, parents give their children to God, and God makes them part of his covenant family, and then gives them back to the parents to raise, nurture, and discipline, as his own holy seed.
It is very fitting to have these baptisms on Easter Sunday because every baptism is an Easter event. Baptism is Easter in sacramental form. In fact, we can really say baptism is Holy Week in sacramental form. The Apostle Paul says in Romans 6 that in baptism we are united to Christ in his death and resurrection. In other words, the one being baptized goes through Good Friday and Easter Sunday at the same time, dying to sin and entering a new life.
Today, these children will be given a new identity, new name, new privileges, and new responsibilities. They will die to sin and rise to a new kind of life. God will become their God and they will become part of his covenant family.