What is God's promise concerning Baptism?

It is given in the words of Christ in the sixteenth chapter of Mark:

"He that believeth and is baptized shall be saved; but he that believeth not shall be condemned."

How can water do such great things?

It is not water indeed that does it, but the Word of God, which is in and with the water, and faith which trusts this Word of God in the water.

For without the Word of God, the water is water alone, and no Baptism. But with the Word of God it is a Baptism, that is, a gracious water of life and a washing of regeneration in the Holy Ghost; as Paul says in the third chapter of the epistle to Titus:

"According to His mercy He saved us, by the washing of regeneration, and renewing of the Holy Ghost; which He shed on us abundantly through Jesus Christ our Savior; that being justified by His grace, we should be made heirs according to the hope of eternal life."

What does the baptizing with water signify?

It signifies that the old man in us should, by daily sorrow and repentance, be drowned and die, with all sins and evil desires; and again a new man daily appear more and more, who shall live before God in righteousness and purity forever.