What does Acts 9:15 mean?

Jesus is telling a disciple in Damascus, named Ananias, to find a traveler named Saul and heal his temporary blindness. Ananias is dubious; he knows this Saul is on a mission to find all Jewish Jesus-followers, arrest them, and take them back to Jerusalem for trial for blasphemy (Acts 9:1–3).

Jesus reveals why He wants Ananias to go. He had commissioned the apostles to be His "witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth" (Acts 1:8). Saul will help with the "end of the earth" part.

Saul's primary mission will be to Gentiles, but he will typically start by reaching out to Jews. Luke will record three of his extensive missionary journeys. It's thought he had a fourth. At each new city, Saul (then going by the Greek version of his name, Paul) goes to the synagogues or, if there are not enough Jews for a synagogue, the place where Jews gather to pray. There, he will explain how Jesus of Nazareth perfectly matches what is written in the Hebrew Scriptures about the Messiah. Some Jews and Gentiles who worship the Jewish God will believe. Others won't, and Saul will be regularly kicked out of the synagogues.

Saul will speak with several leaders, as well. The first stop of his first missionary trip is to the island of Cyprus, where he will speak with the proconsul, Sergius Paulus (Acts 13:7–12). After Saul is arrested in Jerusalem, he will willingly tell his story to Governor Felix (Acts 24:10–21). When Felix is replaced by Festus, Saul seems to lose his patience (Acts 25:1–12), but when Festus entertains Herod Agrippa, Saul will happily share Jesus with the king (Acts 26).