Confirmation is one of the seven sacraments. With Baptism and Eucharist, it is also one of the three sacraments of initiation. Today, as in early Christianity, all three are received at the Easter Vigil following a period of preparation (RCIA).
Confirmation is not as clear in Scripture nor in early Christianity as is Baptism, for example. However, there is evidence for it.
Laying on of hands
In Acts, some who were baptized seem not to have received the fullness of the Spirit until the "laying on of hands' by one of the Apostles. In the early Church, there appears to have been a post-baptismal anointing in some places but not in others. However, the Church has developed a complete ritual utilizing Jewish and early Christian practices. The catechism is a good source of information on Confirmation to help one see the beauty and the meaning of this sacrament, sometimes not fully appreciated.
The rite of Confirmation includes 1) the laying on of hands, 2) the anointing with holy oil (chrism), and 3) the prayer: "Be sealed with the gift of the Holy Spirit," invoking the Holy Spirit's coming. Each of these has special significance.
The bishop is the usual minister of this sacrament. He places his hands over the heads of those being confirmed as did the Apostles so the fullness of the Spirit may come upon those being confirmed.
In the Bible, oil has a rich meaning. It was used to anoint kings who were then graced by God to lead the people in a holy life.
In Confirmation, the anointing with chrism (oil blessed by the bishop during Holy Week) is a sign of consecration which enables followers of Jesus to live a holy life and share in Jesus' mission to lead others to a fuller Christian life.
Athletes too were anointed with oil to make their limbs more flexible and improve their performance. For those confirmed, their whole being is now made stronger and more flexible so that they may be able to live as Jesus did.
In the Old Testament, oil is also a sign of abundance and joy. Those confirmed now have the greatest gift possible and, out of that abundance of love and joy, they will give to God and neighbour.
By the anointing, those being confirmed receive the "seal" or the mark of the Holy Spirit. Seals were used to show ownership. On letters, a seal showed that the seal's owner really sent the letter. The seal shows our belonging to Christ and membership in his body. It shows through Confirmation that we now belong to the Church to serve Christ in his people. We are forever branded as Christ's and therefore, we can be baptized only once.
The Holy Spirit
The most important effect of the sacrament is the outpouring of the Holy Spirit as at Pentecost.
Think of the effects on Jesus' disciples. They changed from fearful people hiding behind locked doors to immediately and boldly going to the Temple, preaching Jesus to those who had crucified him only a few weeks earlier.
That same effect comes in Confirmation. The Spirit gives an abundance of courage (that's where "soldier" came from, though it's not used in the catechism). The Gospels often speak of Jesus being full of the Spirit and being led by the Spirit.
Those confirmed having received the fullness of that same Spirit, will be filled with, and led by, the Spirit to do God's work.
The gifts of the Holy Spirit: wisdom, understanding, knowledge, counsel, piety, fortitude and fear of the Lord will give them the wisdom and strength to live fully their Christian life as adult, responsible members of Christ's Church. Therefore, this sacrament completes their initiation into Christ and the Church, ready to serve God and others.