This act is called a “tonsure” (from the Latin word meaning “to clip” or “to cut”) and takes place near the end of the baptismal service proper. The priest cuts the hair on the front, back, and two sides of the infant’s head, which forms a cross. These hairs are then burnt in the baptismal candle and, in a sense, become the child’s very first offering unto God as an expression of gratitude and thanksgiving for the blessings they have received through the Sacraments and entrance into the Church.
The cutting and offering of hair is symbolic of a lamb which, has only its wool to offer its master and also, per the Old Testament story of Samson, symbolizes ones strength. Therefore, through this act the child pledges to offer its strength to Almighty God.
Fr. Schmemann makes special note that this cutting of hair “is a sign that the life which now begins is a life of offering and sacrifice.” Because of this, the same method of tonsure is used in the consecration of a monastic (monk or nun) – reminding them of the total sacrifice and commitment they now give unto God.