From the CCC:
1288 "From that time on the apostles, in fulfillment of Christ’s will, imparted to the newly baptized by the laying on of hands the gift of the Spirit that completes the grace of Baptism. For this reason in the Letter to the Hebrews the doctrine concerning Baptism and the laying on of hands is listed among the first elements of Christian instruction. The imposition of hands is rightly recognized by the Catholic tradition as the origin of the sacrament of Confirmation, which in a certain way perpetuates the grace of Pentecost in the Church."99
1289 Very early, the better to signify the gift of the Holy Spirit, an anointing with perfumed oil (chrism) was added to the laying on of hands. This anointing highlights the name “Christian,” which means “anointed” and derives from that of Christ himself whom God "anointed with the Holy Spirit."100 This rite of anointing has continued ever since, in both East and West. For this reason the Eastern Churches call this sacrament Chrismation, anointing with chrism, or myron which means “chrism.” In the West, the term Confirmation suggests that this sacrament both confirms baptism and strengthens baptismal grace. *
Two traditions: East and West*
1290 In the first centuries Confirmation generally comprised one single celebration with Baptism, forming with it a “double sacrament,” according to the expression of St. Cyprian. Among other reasons, the multiplication of infant baptisms all through the year, the increase of rural parishes, and the growth of dioceses often prevented the bishop from being present at all baptismal celebrations. In the West the desire to reserve the completion of Baptism to the bishop caused the temporal separation of the two sacraments. The East has kept them united, so that Confirmation is conferred by the priest who baptizes. But he can do so only with the “myron” consecrated by a bishop.101
1291 A custom of the Roman Church facilitated the development of the Western practice: a double anointing with sacred chrism after Baptism. The first anointing of the neophyte on coming out of the baptismal bath was performed by the priest; it was completed by a second anointing on the forehead of the newly baptized by the bishop.102 The first anointing with sacred chrism, by the priest, has remained attached to the baptismal rite; it signifies the participation of the one baptized in the prophetic, priestly, and kingly offices of Christ. If Baptism is conferred on an adult, there is only one post-baptismal anointing, that of Confirmation.
1292 The practice of the Eastern Churches gives greater emphasis to the unity of Christian initiation. That of the Latin Church more clearly expresses the communion of the new Christian with the bishop as guarantor and servant of the unity, catholicity and apostolicity of his Church, and hence the connection with the apostolic origins of Christ’s Church.