Baptism, the Eucharist, and the sacrament of Confirmation together constitute the sacraments of Christian initiation, whose unity must be safeguarded. It must be explained to the faithful that the reception of the sacrament of Confirmation is necessary for the completion of baptismal grace. For by the sacrament of Confirmation, the baptized are more perfectly bound to the Church and are enriched with a special strength of the Holy Spirit. Hence they are, as true witnesses of Christ, more strictly obliged to spread and defend the faith by word and deed. (Catechism #1285)
The effect of the sacrament of Confirmation is the special outpouring of the Holy Spirit as once granted to the apostles on the day of Pentecost.
From this fact, Confirmation brings an increase and deepening of baptismal grace:
Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the "character," which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness.
This character perfects the common priesthood of the faithful, received in Baptism, and "the confirmed person receives the power to profess faith in Christ publicly... (Catechism #1302-1305)
Living Our Vocation as Christians
The confirmed Christian—whether we call him a spiritual soldier or a spiritual adult—goes forth joyfully in the fulfillment of his vocation.
Strong in his faith and with an ardent love for souls which stems from his love for Christ, he feels a continual concern for others. He feels a restless discontent unless he is doing something worthwhile for others—something to ease their burdens in this life, and something to make more secure their promise of life eternal.
His words and his actions proclaim to those around him: “Christ lives, and He lives for you.”
The grace to do this is the grace which Jesus promised to His Apostles (and to us) when He said: “You shall receive power when the Holy Spirit comes upon you, and you shall be witnesses for Me… . even to the very ends of the earth” (Acts 1:8). (Borrowed with modifications from http://www.beginningcatholic.com/confirmation.)