Peter's response contained two inspired conditions that are applicable to anyone who is a believer in Jesus Christ (as they were at that point) and wanting to be forgiven: (1) Repent and (2) Be baptized. The use of the conjunction "and" makes it clear that both of these conditions need to be met if one's sins are to be remitted and if one is to receive the gift of the Holy Spirit. Had these individuals not yet had faith in Christ, such would have also been commanded (cf. Acts 16:30,31).
Although many believe that repentance is sorrow for sins, this passage implies that it is not. In Acts 2:37 the people were sorrowful, yet Peter commands them to repent in the next verse. Thus, repentance must be something different than sorrow over sin (though godly sorrow should lead to true repentance; cf. II Cor. 7:9,10). If repentance is not sorrow over sin, then what is it? Repentance is a change of mind that will lead to a change of behavior. It is a turning from wickedness to righteousness. This change of mind is based upon sincere, godly sorrow for past sins. The New Testament stresses the importance of repentance in other passages also (e.g., Luke 13:3,5; Acts 17:30,31). Although few question the need for repentance, many question the necessity of the second condition Peter declared here--baptism for the remission of sins.
For those who are unbiased and willing to accept plain declarations of Scripture, Acts 2:38 alone should be enough to quench those objections--not to mention the other New Testament passages that can be consulted (e.g., Mark 16:16; Acts 22:16; I Pet. 3:21; Col. 2:12,13; Gal. 3:27 coupled with II Tim. 2:10; etc.). Peter commanded that they repent and be baptized (i.e., immersed in water) "for the remission of sins." Although many have labored long and hard to deny (by twisting) the clear meaning of this phrase (cf. II Pet. 3:16), such efforts are futile and the truth of God's word remains. If Peter had not wanted to communicate the necessity of baptism to receiving the forgiveness of sins, then he would not have declared such on this occasion! He would have spoken differently if he had only wanted to convey the necessity of repentance for believers. Those on Pentecost who developed faith in Christ were instructed to repent and be baptized in order to obtain forgiveness, and that is precisely what they did (as the rest of Acts 2 explains). Those who teach that forgiveness comes at the point of faith prior to baptism are teaching something that the apostles never taught (and our continued studies in the book of Acts will make this crystal clear).
Baptism is to be done "in the name of Jesus Christ." In other words, baptism is to rest or rely upon His authority and the fact that He is the great Savior and King. Jesus Christ is the foundation of baptism (cf. Rom. 6).
There is much more that could be considered on baptism and the various objections many offer against its importance in the securing of forgiveness. We have only presented some of the basic principles in this lesson. For more in-depth study on baptism as it relates to salvation, please consult our three-part topical study on baptism from 03/12/05, 03/19/05, and 03/26/05 as well as three other related studies from 07/30/05, 11/19/05, and 10/31/08.