What does Acts 13:33 mean?
Paul and Barnabas are visiting a synagogue in Pisidian Antioch, slightly southwest of the center of modern-day Asia Minor. Paul is explaining how the salvation God has always given Israel is deepening. Throughout Israel's history, God has saved them from slavery, hardships, starvation, and enemies. With the death and resurrection of Jesus, God offers to save them from their sins and to a reconciled relationship with Him, as He promised the Jewish fathers. This "good news" has come to the children of the patriarchs (Acts 13:32).In this section, Paul is showing how the resurrection of God's promised Savior (Acts 13:23–25, 27, 30) was promised in Jewish prophecy. In this quote from the Septuagint, he shows the relationship between God and that Savior—Jesus is the Son of God the Father.
There is an on-going discussion as to what "raising Jesus" means. Most commentators believe it does not refer to the resurrection (which will be addressed in Acts 13:34–35) but to God's overall act of presenting Jesus to the world and endowing Him to be the Savior of the world. The quote of Psalm 2:7 doesn't refer specifically to Jesus' baptism wherein God declared Jesus His "beloved" Son (Matthew 3:17) or to the transfiguration where, again, God called Jesus His "beloved" Son (Mark 9:7). It's the broader sense of Jesus' whole ministry and mission as described in John 3:16.
"Begotten" is from the Greek root word gennao, which literally means "to give birth to something," which could infer the work of the Holy Spirit who impregnated Mary. In Psalm 2:7 and John 3:16, it refers more generally to the act of causing something to come into being. What it doesn't mean is the false teaching that God created the Son. God arranged for the Son to have a human body, a human nature, and live a human life with a beginning and an earthly end. But the Son is co-eternal with the Father. Jesus as God was not created. What God begat or started was God the Son's role as the heir of David, the Messiah of the Jews, and the Savior of the world.
There is a sense in which God begat Jesus at the point of His resurrection. When a Jewish king was crowned, the moment was considered to be the start of a new relationship between God and the king—a relationship of sonship. With Jesus' resurrection, He took His place as eternal king in David's line. His kingship is "already but not yet," meaning He is king in a spiritual sense, but He will not be physical king over the earth until the millennial kingdom.
Pisidian Antioch was home to a big temple to Caesar Augustus, whom the people worshiped as a god. Now, Paul is saying Jesus is the Son of God. Augustus was known as the "son of the deified," the "deified" being Julius: divi filius. Augustus was also called as "savior." Paul's audience would not believe that the emperor was the son of God, but it's still interesting how Paul uses the local vernacular to make his point.