Peter continues his speech that he began in Acts 3:12 to the Jews who stood in the temple area.
In verses 22-23 Peter quotes something Moses told before the Messiah came.
"He is the One heaven must welcome." Peter speaks of heaven as if it were a person who welcomes Jesus into his home. (See: rc://en/ta/man/translate/figs-personification)
This means that it is necessary for Jesus to remain in heaven because that is what God has planned.
Possible meanings are 1) "until the time when God will restore all things" or 2) "until the time when God will fulfill everything that he foretold."
When the prophets spoke long ago, it was as if God himself was speaking because he told them what to say. AT: "about which things God spoke long ago by telling his holy prophets to speak about them"
Here the word "mouth" refers to the words that the prophets spoke and wrote down. AT: "the words of his holy prophets" (See: rc://en/ta/man/translate/figs-metonymy)
"Raise up" here is an idiom for "establish." AT: "God will establish a prophet" (See: rc://en/ta/man/translate/figs-idiom)
This can be stated in active form. AT: "that prophet, God will completely destroy" (See: rc://en/ta/man/translate/figs-activepassive)