Confirmation is one of the seven recognized Sacraments of the Roman Catholic Church. When one is baptised as an infant, one is a full member of the Church; however at confirmation the person's relationship with the church as well as with Christ and the Holy Spirit is made "more perfect." One thereby becomes a true witness of Christ. Additionally, one receives special strength from the Holy Spirit to do God's work. It also deepens and increases the grace of God received at Baptism. It normally is conferred at the "age of discretion," when one is deemed capable of understanding the nature of his actions.
To see the importance of confirmation in the Catholic Church, remember that Catholics are baptized as infants, not as adults the way many Protestant sects do things. Because of this, confirmation is an important way for the teen (now an adult in many ways) to reaffirm the promises that were made on his or her behalf at baptism.
At a Catholic baptism, the parents and godparents of the child make various promises on the child's behalf. They promise, for example, to reject Satan and all his works. The child cannot, of course, participate. When a child is 6 or 7 and takes Holy Communion, they are participating more fully in the Church but are still really not old enough to fully understand their commitment to the Church.
By the time that a person is confirmed, they are old enough to really make a commitment for themselves. This is the importance of confirmation -- to commit yourself to God and the Church in a way that was not possible at the time you were baptized.