Confirmation is a hard sacrament to explain. 

It's NOT a coming of age thing--although most people think it is. 

It can be given at a variety of ages; in some places, it's given before First Holy Communion; in some places, it's not given until sixteen years of age. Parishes within the same diocese vary greatly: at my current parish, it's given in sixth grade; at my parochial school, it was eighth grade; at the parish in my parents' town, it's 10th grade. 

What is going on?! 

Let's try to get down to basics. 

In Confirmation, the confirmand (person to be confirmed) receives the gifts of the Holy Spirit. 

We've talked about form and matter previously. So here, the form is the bishop (or designated priest, if the bishop can't perform the sacrament for some reason) saying, "be sealed with the gift of the Holy Spirit." The matter is the holy chrism (Which is also used in baptism), which is placed on the confirmand's forehead in the sign of the cross. 

The Scriptural basis for Confirmation is from the Acts of the Apostles: 

Now when the apostles, who were in Jerusalem, had heard that Samaria had received the word of God, they sent unto them Peter and John. Who, when they were come down, prayed for them, that they might receive the Holy Ghost.For he was not as yet come upon any of them; but they were only baptized in the name of the Lord Jesus. Then they laid their hands upon them, and they received the Holy Ghost.-- Acts, 8:14-17. 

In Confirmation, the Confirmand also received the gifts of the Holy Spirit. There are seven of them. Confirmation gives the confirmand strength to live out their Christian vocation and their specific calling. 

The confirmand also chooses a patron saint. The Church asks that a baby be baptized with the name of at least one saint (my name is two--there's a St. Emily, and Michele is the feminine form of Michael--St. Michael the Archangel.). However....that doesn't always happen. In Confirmation, the confirmand selects a saint that is meaningful to them. I chose St. Therese of Lisieux. 

Confirmation completes the sacraments of initiation. At this point, you are an "adult" in the sense that you are fully "initiated" into the church, having had all three sacraments of initiation (Baptism, Communion, and Confirmation).