The word "Blessing" has various meanings. See Catechism 1078-1079;1669;167-172.
It means to adore, to praise God, as when we bless God. Ex. Psalm 34.
In the liturgical sense, blessing is a rite than contains a ceremony and prayers to invoke God's good in the name and with the authority of the Church. It is performed by an ordained minister. Things are also blessed to dedicate them to Divine service or to ask God that they may be under His protection.
Lay persons, in virtue of their union with God, can also bless in a simple manner, such as saying: "May the Lord bless you". There is a particular significance in the blessing of parents to their children since God has entrusted them to transmit his love.
Can women bless priests? Certainly!
Some Catholic sites have criticized the Cardinal for asking a woman who is not fully in communion with the Catholic faith to bless him. However, the Cardinal acted according to Catholic teaching. The baptism of Protestants, if performed with water in the name of the Trinity, is valid. This means that Catholics and Protestants share the same baptism. That is why we do not baptize them when they come to full communion in the Catholic Church. Renewing our baptism commitment in an ecumenical service is a sign of unity in Christ and therefore, of the love we must share as we continue to work and suffer for the sake of full communion.
The love of Jesus for those who were not fully living the Jewish faith scandalized some. They could not understand that love is the only force that heals and brings light to darkened souls. What Cardinal O'Malley did is an act of humility and love in imitation of Christ who allowed a woman to kiss and anoint His feet. Blessing and allowing others to bless us is not an act of judgment; it is an act of love.