Through the sacrament of Chrismation (called Confirmation in the Western Church) we receive the gifts of the Holy Spirit and confirm our baptismal promises. Greater awareness of the grace of the Holy Spirit is conferred through the anointing of chrism oil and the laying on of hands by the Bishop.
Confirmation perfects Baptismal grace; it is the sacrament which gives the Holy Spirit in order to root us more deeply in the divine filiation, incorporate us more firmly into Christ, strengthen our bond with the Church, associate us more closely with her mission, and help us bear witness to the Christian faith in words accompanied by deeds. (CCC 1316)
As we read in the Lumen Gentium (the Dogmatic Constitution of the Church) from the Second Vatican Council:
Bound more intimately to the Church by the sacrament of confirmation, [the baptized] are endowed by the Holy Spirit with special strength; hence they are more strictly obliged to spread and defend the faith both by word and by deed as true witnesses of Christ. (no. 11)
In the Acts of the Apostles we read of the coming of the Holy Spirit on Pentecost. While baptism is the sacrament of new life, confirmation gives birth to that life. Baptism initiates us into the Church and names us as children of God, whereas confirmation calls us forth as God’s children and unites us more fully to the active messianic mission of Christ in the world.
After receiving the power of the Holy Spirit at Pentecost, the Apostles went out and confirmed others, showing confirmation to be an individual and separate sacrament: Peter and John at Samaria (Acts 8:5-6, 14-17) and Paul at Ephesus (Acts 19:5-6). Also the Holy Spirit came down on Jews and Gentiles alike in Caesarea, prior to their baptisms. Recognizing this as a confirmation by the Holy Spirit, Peter commanded that they be baptized (Acts 10:47).