See the notes at Matthew 3:3, Matthew 3:5-6, Matthew 3:11.

John - The original name is nearly lost in the Greek Ιωαννης, and in the Latin Johannes, and almost totally so in the English John. The original name is יהוחנן Yehochanan, compounded of יהוה חנן Yehovah chanan, the grace or mercy of Jehovah: a most proper and significant name for the forerunner of the God of All Grace. It was John's business to proclaim the Gospel of the grace of God, and to point out that Lamb or sacrifice of God which takes away the sin of the world.
For the remission of sins - Or, toward the remission - εις αφεσιν. They were to repent, and be baptized in reference to the remission of sins. Repentance prepared the soul for it, and Baptism was the type or pledge of it. See on Matthew 3:2 (note).

(2) John did baptize in the wilderness, and preach the (d) baptism of repentance for the remission of sins.
(2) The sum of John's doctrine, or rather Christ's, is remission of sins and amendment of life.
(d) The Jews used many kinds of washings: but here a peculiar kind of washing is spoken of, which contains within it true baptism, amendment of life, and forgiveness of sins.

John did baptize in the wilderness,.... Of Judea, Matthew 3:1, where he first appeared as a preacher; and is the same wilderness Isaiah has respect to in the above prophecy, Isaiah 40:3. The words are best rendered in the Vulgate Latin and Syriac versions; "John was in the wilderness, baptizing and preaching the baptism of repentance, for the remission of sins": according to which, the account of the Baptist begins with his name, John; describes the place where he was where he made his first appearance, and continued in, the wilderness; which was not a wild uninhabited place and without people, but had many cities, towns, and villages in it; and also declares his work and ministry there, which was preaching and baptizing: for though baptizing is here put before preaching, yet certain it is, that he first came preaching in these parts; and there baptized such, to whom his preaching was made useful. Baptism is here called, the
baptism of repentance: because John required repentance antecedent to it, and administered it upon profession of repentance, and as an open testification of it; and this
for, or
unto the remission of sins: not for the obtaining the remission of sins, as if either repentance, or baptism, were the causes of pardon of sin; but the sense is, that John preached that men should repent of their sins, and believe in Christ, who was to come; and upon their repentance and faith, be baptized; in which ordinance, they might be led to a fresh view of the free and full forgiveness of their sins, through Christ; whose blood was to be shed for many, to obtain it: see Acts 2:38.

John did baptize in the wilderness. Of Judea. See note on Matthew 3:1, for account of the wilderness and John the Baptist.
And preached the baptism of repentance. He preached, as well as baptized. Only those who repented were fit subjects of baptism. Hence it was called the "baptism of repentance." Repentance signifies, not only sorrow for sin, but the resolve to sin no more.
For remission of sins. This indicates the object of repentance and baptism. Those who repented and were baptized were pardoned. Both were needful to remission. Compare Acts 2:38.

Preaching the baptism of repentance - That is, preaching repentance, and baptizing as a sign and means of it.