What is baptism?

Westminster Larger Catechism

Q. 165. What is baptism?
A. Baptism is a sacrament of the New Testament, wherein Christ hath ordained the washing with water in the name of the Father, and of the Son, and of the Holy Ghost,[1058] to be a sign and seal of ingrafting into himself,[1059] of remission of sins by his blood,[1060] and regeneration by his Spirit;[1061] of adoption,[1062] and resurrection unto everlasting life;[1063] and whereby the parties baptized are solemnly admitted into the visible church,[1064] and enter into an open and professed engagement to be wholly and only the Lord's.[1065]

Q. 166. Unto whom is baptism to be administered?
A. Baptism is not to be administered to any that are out of the visible church, and so strangers from the covenant of promise, till they profess their faith in Christ, and obedience to him,[1066] but infants descending from parents, either both, or but one of them, professing faith in Christ, and obedience to him, are in that respect within the covenant, and to be baptized.[1067]

Q. 167. How is our baptism to be improved by us?
A. The needful but much neglected duty of improving our baptism, is to be performed by us all our life long, especially in the time of temptation, and when we are present at the administration of it to others;[1068] by serious and thankful consideration of the nature of it, and of the ends for which Christ instituted it, the privileges and benefits conferred and sealed thereby, and our solemn vow made therein;[1069] by being humbled for our sinful defilement, our falling short of, and walking contrary to, the grace of baptism, and our engagements;[1070] by growing up to assurance of pardon of sin, and of all other blessings sealed to us in that sacrament;[1071] by drawing strength from the death and resurrection of Christ, into whom we are baptized, for the mortifying of sin, and quickening of grace;[1072] and by endeavoring to live by faith,[1073] to have our conversation in holiness and righteousness,[1074] as those that have therein given up their names to Christ;[1075] and to walk in brotherly love, as being baptized by the same Spirit into one body.[1076]

Source: Daily Confession