What does Acts 2:32 mean?

Peter is using a psalm of David to show that Jesus is David's heir and the Messiah promised by God. In Psalm 16:8–11, David identifies his "Lord" as someone whose body will not decay in death (Psalm 16:8, 10; Acts 2:25, 27). This is about fifty days after Jesus was crucified and His disciples claimed He rose from the dead.

The witnesses Peter is referring to are the 120 who remained in Jerusalem and received the Holy Spirit (Acts 1:15; 2:1–4). In the forty days between Jesus' resurrection and ascension to heaven, He saw Mary Magdalene (John 20:11–18), the disciples minus Thomas (John 20:19–23), the disciples with Thomas (John 20:24–29), Cleopas and a friend (Luke 24:13–35), Judas' replacement Matthias (Acts 1:22), His half-brother James (1 Corinthians 15:7), and five hundred unnamed followers (1 Corinthians 15:6).

About nine days before Peter's speech, minutes before Jesus ascended into heaven, Jesus told His disciples, "But you will receive power when the Holy Spirit has come upon you, and you will be my witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth" (Acts 1:8). Earlier this morning, they received the Holy Spirit (Acts 2:1–4). Now they're fulfilling their commission as witnesses in part by speaking the different languages and dialects represented in the crowd (Acts 2:5–13).

The 120 know that they are to bear witness to the truth about Jesus—His miraculous works, that He is the Messiah, and that His death and resurrection wipes out the sins of those who follow Him. But they don't know that martys, the Greek word for "witness," will subtly alter in its application. That change will result in the meaning of the modern English word "martyr." Of the twelve apostles, church tradition says all but John will die a martyr's death. Jesus has already warned Peter he will be crucified (John 21:18–19). Legend says Peter refused to die in the same way as his Master and insisted on being hanged upside-down. Only John will die of natural causes, but, legend says, only after surviving a cauldron of burning oil.