John Gill Commentary Acts 13:38

"Be it known unto you therefore, brethren, that through this man is proclaimed unto you remission of sins:" — Acts 13:38 (ASV)

Be it known to you, therefore, men and brethren
The apostle having discussed about the incarnation of Christ, his death and resurrection, proceeds to take notice of some particular benefits and blessings of grace arising from that, which are published and made known to the sons of men in the everlasting Gospel, as they were now to the Jews by Paul and Barnabas; such as forgiveness of sins through the blood of Christ, and justification by his righteousness; the former is mentioned in this verse, the latter in the next:

that through this man is preached to you the forgiveness of sins ;
forgiveness of sins, which is sometimes expressed by a non-imputation of them, a non-remembrance of them, a covering and putting them away, and a blotting them out, is an act of free grace and mercy, and yet is through the blood of Christ; through that believers have forgiveness; Christ is exalted as a Prince and a Saviour to give forgiveness, having by his blood procured forgiveness; and this is a principal doctrine of the Gospel, which is published in Christ's name, and which the light of nature and law of Moses know nothing about, and cannot confirm; the prophets testify to this truth, that everyone who believes in Christ shall receive the remission of sins, of all his sins.

That there is a God is known by the light of nature, and that sin is an offence to him; but by it it is not known in what way the offended Deity is appeased; nor does it, nor can it assure anyone that God will forgive sin on any account whatever; not on account of mercy in God, nor on account of good works, or of repentance in people; God, as the God of nature, does not forgive sin, but as the God of grace:

and though the law of Moses declares what is good, and gives knowledge of evil, yet does not admit of repentance as a satisfaction for sin committed; nor does it represent God as merciful, but as just, and so accuses, condemns, and kills: the doctrine of forgiveness is a pure doctrine of the Gospel; and when it is preached correctly, it is preached through Christ, not through the works of the law, not through repentance, nor through faith, nor through the absolute mercy of God, but through Christ, through the blood of Christ, which was shed to obtain forgiveness in a way consistent with the justice of God; and through Christ's hands it is given.

When Christ is called a "man", it must not be thought that he is a mere man; he is God as well as man; had he been a mere man, forgiveness of sin could not have been by his blood, or through his name, or for his sake; it is because he is God, truly and properly God, that there is a virtue in his blood to take away sin, and cleanse from it; see (1 John 1:7) Besides, the word "man" is not in the original text, it is only "through this is preached to you"; that is, through this glorious and divine person, who, though he died as man, and was buried, yet saw no corruption, and is now raised from the dead, and is at the right hand of God. Some copies read (dia touto) , because of this, or for this reason; seeing he is raised from the dead, therefore the doctrine of the remission of sins is preached; for if he had died, and had not risen again, there could have been no pardon by his blood, nor justification by his righteousness; see (Romans 4:25) .