What does Acts 9:29 mean?

"Hellenist" is from a term referring to an ancient Greek. "Hellenist" is used as a generic adjective to describe someone or something culturally Greek. So, a "Hellenist Jew" is a Jewish person who was born in an area highly influenced by Greco-Roman culture. This would contrast with Jews born and raised in Judea, Samaria, Galilee, Perea, or other areas near Jerusalem. Hellenist Jews typically spoke Greek as their first language and generally didn't have a problem with the Roman Empire. Theologically, many adopted the Greek rejection of a resurrection. They had their own synagogues in Jerusalem and those who didn't live near Jerusalem did not attend all the required feasts, although they still venerated Jerusalem and the temple.

Hellenist Jews often moved to Jerusalem when they grew older, as they wished to die and be buried near the City of David. It was these widows who received insufficient support from the mostly-Hebrew-cultured Jewish Jesus-followers. The apostles' solution was to appoint deacons to distribute the food; considering their names, it's thought all the deacons were Hellenists (Acts 6:1–6).

Stephen was one of those deacons, but he was also a powerful apologist who preached that Jesus is the Jewish Messiah to the Hellenist synagogues in Jerusalem (Acts 6:8–15). The Jews strongly opposed Stephen, in part because he preached the resurrection of the dead and probably in part because he seemed to disrespect the religion these men followed even in the hostile, pagan cities in which they lived. When they couldn't refute Stephen's arguments, they accused Stephen of blasphemy and then murdered him while a young man named Saul looked on (Acts 7).

Saul is also a Hellenist; he is from the city of Tarsus on the coast of modern-day Asia Minor, although he went to school in Jerusalem (Acts 22:3). All the apostles are Jewish, from Galilee, so it's natural that Saul concentrated on the Hellenist Jews. Unfortunately, he received the same reception as Stephen. Jesus has already told him he will be the missionary to the Gentiles (Acts 26:16–18); now, while praying at the temple, Jesus tells him to leave Jerusalem because he won't be accepted (Acts 22:17–18).

All is not in vain, however. There were some Hellenist Jews listening to Peter and the other apostles before Saul's conversion. When Saul started persecuting the church, they fled north to Syrian Antioch where they not only spread the message to other Jews, they told Gentiles. Soon, Barnabas will travel to Antioch to validate the Gentiles' conversion. He will find such a need of teachers he will send for Saul, who has returned to Tarsus (Acts 11:19–26).