"Confirmation completes the grace of Baptism by a special outpouring of the gifts of the Holy Spirit, which seal or 'confirm' the baptized in unison with Christ and equip them for active participation in the worship and apostolic life of the Church" (The Glossary of the Catechism of the Catholic Church).
Holy Baptism is the first sacrament of initiation, and Confirmation is the second. By Confirmation (or Chrismation as it is called in the Christian East), the baptized are more perfectly bound to the Lord Jesus and His Church, and they are enriched with a special strength of the Holy Spirit to be witnesses (or martyrs) of Christ and the truth of His Gospel.
On several occasions in His preaching, the Lord Jesus promised an outpouring of God the Holy Spirit on His disciples, and this promise was fulfilled first on the Day of Resurrection and then more strikingly at Pentecost. St. Peter declared this outpouring of the Holy Spirit to be the sign of the messianic age. From that time on and in fulfillment of Christ's command, the Apostles imparted to the newly baptized by the laying on of hands the gift of the Holy Spirit to complete the grace of Baptism.
The imposition of hands, therefore, is the origin of the sacrament of Confirmation which perpetuates the grace of Pentecost in the Church. Very early in the Church's life this apostolic laying on of hands was accompanied by an anointing with perfumed oil called sacred chrism, the better to signify the gift of the Holy Spirit Who anointed the Lord Jesus at His own Baptism. This anointing highlights the name Christian, which derives from the sacred title of Messiah (or Christ from the Greek translation), meaning "the Anointed One."
In the Eastern Churches (both Catholic and Orthodox), Confirmation or Chrismation is administered together with Baptism, even to infants. But in the Western Church, the two first sacraments of initiation became separated in the early Middle Ages, and to this day Confirmation is administered after the age of reason for those baptized as infants.
For adult converts who have never been baptized, the unity of these two sacraments is now restored when they are given together at the Easter Vigil. All Catholic Christians should receive the Sacrament of Confirmation to complete their communion with Christ and be marked by the perfection of the baptismal priesthood of the faithful in order to proclaim more boldly and publicly that Jesus Christ is Lord. Any baptized adult Catholic who has not yet been confirmed should participate in the Rite of Christian Initiation of Adults (RCIA) and receive the Sacrament of Confirmation at Easter.