What is the meaning of Acts 2:39?

For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call. (Acts 2:39 KJV)

For to you is the promise, and to your children, and to all that are afar off, [even] as many as the Lord our God shall call unto him. (Acts 2:39 ASV)

For to you is the promise and to your children, and to all who [are] afar off, as many as [the] Lord our God may call. (Acts 2:39 DBY)

for to you is the promise, and to your children, and to all those afar off, as many as the Lord our God shall call.'(Acts 2:39 YLT)

For to you is the promise, and to your children, and to all who are far off, even as many as the Lord our God will call to himself.” (Acts 2:39 WEB)

Interlinear

For <gar> the promise <epaggelia> is <esti> unto you, <humin> and <kai> to your <humon> children, <teknon> and <kai> to all <pas> that are afar off <eis>, <makran> even as many as <hosos> the Lord <kurios> our <hemon> God <theos> shall call <an>. <proskaleomai> (Acts 2:39 KJV)

Albert Barnes

Verse 39.  For the promise. That is, the promise respecting the particular thing of which he was speaking–the influences of the Holy Ghost. This promise he had adduced in the beginning of his discourse, (Ac 2:17,) and he now applies it to them. As the Spirit was promised to descend on Jews and their sons and daughters, it was applicable to them in the circumstances in which they then were. The only hope of lost sinners is in the promises of God; and the only thing that can give comfort to a soul that is convicted of sin, is the hope that God will pardon and save.

To you. To you Jews, even though you have crucified the Messiah. The promise had especial reference to the Jewish people.

To your children. In Joel, to their sons and daughters, who should, nevertheless, be old enough to prophesy. Similar promises occur in Isa 44:3, “I will pour my Spirit upon thy seed, and my blessing upon thine offspring,” and Isa 59:21. In these and similar places, their descendants or posterity are denoted. It does not refer to children as children, and should not be adduced to establish the propriety of infant baptism, or as applicable particularly to infants. It is a promise, indeed, to parents, that the blessings of salvation shall not be confined to parents, but shall be extended also to their posterity. Under this promise parents may be encouraged to train up their children for God; to devote them to his service; believing that it is the gracious purpose of God to perpetuate the blessings of salvation from age to age.

To all. To the whole race; not limited to Jews.

Afar off. To those in other lands. It is probable that Peter here referred to the Jews who were scattered in other nations; for he does not seem yet to have understood that the gospel was to be preached to the Gentiles. See Ac 10:1-48. Yet the promise was equally applicable to the Gentiles as the Jews; and the apostles were afterwards brought to understand it, Ac 10:1-48; Ro 10:12,14-20, Ro 11:1-36. The Gentiles are sometimes clearly indicated by the expression “afar off,” Eph 2:13, Eph 2:17; and they are represented as having been brought nigh by the blood of Christ. The phrase is equally applicable to those who have been far off from God by their sins and their evil affections. To them also the promise is extended if they will return.

Even as many, etc. The promise is not to those who do not hear the gospel, nor to those who do not obey it; but it is to those to whom God, in his gracious Providence, shall send it. He has the power and right to pardon. The meaning of Peter is, that the promise is ample, full, free; that it is fitted to all, and may be applied to all; that there is no defect or want in the provisions or promises; but that God may extend it to whomsoever he pleases.  We see here how ample and full are the offers of mercy. God is not limited in the provisions of his grace; but the plan is applicable to all mankind. It is also the purpose of God to send it to all men; and he has given a solemn charge to his church to do it. We can not reflect but with deep pain on the fact that these provisions have been made, fully made; that they are adapted to all men; and yet that by his people they have been extended to so small a portion of the human family. If the promise of life is to all, it is the duty of the church to send to all the message of eternal mercy.

 {a} “promise is unto you” Joe 2:28

{b} “and to all that are afar” Eph 2:13, Eph 2:17