What does Acts 3:20 mean?

When Jesus ascended to heaven, the disciples thought His return would be soon (Acts 1:9). Even Paul (Romans 8:19–25; 1 Corinthians 1:7), James (James 5:8), and Jude (Jude 1:21) likely thought Jesus would return in their lifetimes.

Two thousand years later, we're still waiting. Prophecy in the Bible is almost never about the church age—it is for the nation of Israel. So, in biblical prophecy, there is a gap between Jesus' ascension and the events leading up to the tribulation, with a tiny bit about the destruction of the temple in AD 70. Peter thinks his audience will see Jesus return, even though Jesus told him and the other disciples, "It is not for you to know times or seasons that the Father has fixed by his own authority" (Acts 1:7).

Isaiah describes the "times of refreshing" in Isaiah 61. Israel will be restored; Jesus will free the captives and comfort the mourning. The world will honor the Jews. This will happen during the millennial kingdom when Jesus literally reigns over Israel (Isaiah 2:4; 42:1).

Peter's audience will not live to see that day. The reference here is corporate, meaning it applies to a wider group. Just as the Jews are corporately responsible for Jesus' death (Acts 3:13–15), the Jewish nation will corporately experience the times of refreshing and the reign of their Messiah. This does not mean that only the Jews are responsible for Jesus' death. Everyone who ever sinned is responsible: i.e. everyone. It just happens that Peter is in Jerusalem, speaking to Jews. Later, Paul will warn the Greeks in Athens that judgment is coming for the entire world (Acts 17:31).