Act 2:38-39 Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. (39) For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call."
Hi,
I believe the passage in question refers to the promise of the Holy Spirit, as referenced earlier in the chapter after Peter addresses the claim of drunkeness because of the tongues the disciples were speaking in and the excitement over the sound of a rushing wind and what appeared to be tongues of fire on their heads.
Act 2:16-21 But this is that which was spoken by the prophet Joel; (17) And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams: (18) And on my servants and on my handmaidens I will pour out in those days of my Spirit; and they shall prophesy: (19) And I will shew wonders in heaven above, and signs in the earth beneath; blood, and fire, and vapour of smoke: (20) The sun shall be turned into darkness, and the moon into blood, before that great and notable day of the Lord come: (21) And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved.