Confirmation is one of the three "Sacraments of Initiation" through which the power of the Holy Spirit binds the baptized faithful more perfectly to the priestly, prophetic, and kingly ministry of Christ, the 'anointed one'. As Jesus was overshadowed by the Spirit at his baptism in the Jordan, Christians everywhere were promised an outpouring of the Holy Spirit to be a sign of the messianic age. This Spirit, imparted by baptism and a laying on of hands (see Hebrews 6:2) is a most ancient rite of the Church signifying and perpetuating the grace of Pentecost poured upon the Church. Very early in the history of the Church, in order to better signify the gift of the Holy Spirit, an anointing with perfumed oil (Chrism) was added to the laying on of hands in order to highlight the title "Christian" which means "anointed" (and also from which we get the title "Christ"). The rite of anointing which became known as "Crismation" in the East and "Confirmation" in the West has continued in both Catholic and Orthodox Churches for all these centuries.
In the West, the Sacrament of Confirmation became separated from the Sacrament Baptism in order to preserve the bishop's prerogative to administer this sacrament as part of his apostolic ministry. Baptized Christians receive this sacrament at the hands of their bishop, (or at least by his explicit delegation of a priest by the bishop,) as a sign of the candidate's unity with the authentic, apostolic faith and ministry bestowed on the Church on Pentecost. The title "Confirmation" further suggests that the sacrament both confirms and strengthens baptismal grace through the gift of the Holy Spirit.
The sign of anointing imprints a spiritual seal on those who are Confirmed, marking the Christian in his or her total dedication to Christ and in the eternal promise of divine protection in the time of great eschatological trial (see Revelation 7: 2-4).
The Sacrament of Confirmation is been celebrated at different ages in different places. Indeed, the standard of Church law is set between the "age of reason" (approximately First Communion age) and the age of 16, with final determination left to the discretion of the local bishop or even the pastor. At St. Aloysius, Confirmation is typically celebrated with young men and women of approximately junior high-school age. It is this age when our young people are in special need of the grace to live their lives in witness to the faith they received at Baptism. While Confirmation is not, strictly speaking, a sacrament of Christian maturity, it is an opportunity for our young people to internalize the faith in a way they may not have previously considered as they accept their baptismal call in a new, visible, and public way. Confirmation is also not a sacrament of "graduation", signifying the completion of Christian formation or education. Those who are confirmed are called even more to live a life of conversion, worship, service, and evangelization. Those who do not intend to grow as Christians after receiving Confirmation might want to delay Confirmation or reconsider why they are being confirmed so that they are will not be found responsible for the poor use of God's grace conferred in this sacrament.
Candidates for Confirmation are presented to the Church by a sponsor- one who vouches for the preparation of the candidate and promises to assist them in their Christian growth. It is recommended that sponsors for Confirmation be the same sponsors as were selected for Baptism. For more information about Confirmation Sponsors, please see this document.
Those who come into the Church by way of the Rite of Christian Initiation of Adults are confirmed at the time of their baptism or reception. This is usually done by the pastor at the Easter Vigil.
The Sacrament of Confirmation (from the Catechism of the Catholic Church)
The Church Fathers on Confirmation (via Catholic Answers)
The Seven Gifts of the Holy Spirt (via Catholic Answers)
Confirmation (via the 1917 Catholic Encyclopedia)