This is a very old tradition and the Church encourages parents to do so.
It is the task of parents to bring their children closer to God, as the CCC says:
“Through the grace of the sacrament of marriage, parents receive the responsibility and privilege of evangelizing their children. Parents should initiate their children at an early age into the mysteries of the faith of which they are the ‘first heralds’ for their children”CCC 2225
One vital aspect of this evangelization is an ancient tradition called “Parental Blessing”, which simply means calling down the blessings upon the children. The parents have a responsibility to entrust their children to God every day. This type of blessing is very effective as seen throughout the scriptures. The Old Testament is rife with such examples. The most prominent perhaps is that of Issac blessing his son Jacob in Genesis Chapter 27:
So he went to him and kissed him. When Isaac caught the smell of his clothes, he blessed him and said,
“Ah, the smell of my son is like the smell of a field that the Lord has blessed. May God give you heaven’s dew and earth’s richness— an abundance of grain and new wine. May nations serve you and peoples bow down to you. Be lord over your brothers, and may the sons of your mother bow down to you. May those who curse you be cursed and those who bless you be blessed.” 27-29
Another popular blessing used in the book of Numbers is referred to as the Aaronic Blessing:
“The Lord bless you and keep you. May the Lord let his face shine upon you, and be gracious to you. The Lord look upon you kindly and give you peace” .Numbers 6:24-26
Another one from the book of Tobit:
“May God in heaven protect you on the way and bring you back to me safe and sound; may his angel accompany you”Tobit 5:17
How to perform/say the Blessing:
A very simple way of doing this would be to use holy water if available, trace the sign of the cross on the forehead of the child and say any of the prayers above or simply say “May God bless you in the name of the Father and the Son and the Holy Spirit”. You can also pray spontaneously as there is no formula for this type of blessing.
The situation surrounding this blessing is also important. You can be praying for something specific. Maybe your child is going off to school or is beginning a new chapter in their life. Or your child is sick and restless. You can your words to invoke God’s blessings, recognizing the power that God has given you as a parent and the gift of the Sacraments you receive.
The whole idea is not only to bring the spiritual blessings of God but to offer comfort to your mind and your child’s.
It is never easy being a parent, but calling on God from time to time works wonders in the souls of the children.