What does Acts 26:27 mean?

In a room filled with military tribunes, the civilian leadership of Caesarea Maritima, Paul is calling out King Agrippa II. Also in the audience are Agrippa's sister/lover Bernice and the new governor Festus (Acts 25:23). Paul has presented the gospel in the context of his own conversion story. He has defended himself against charges that he incites riots, profaned the temple, and leads a cult not authorized by the Roman government (Acts 24:5–6; 25:7–8).

During his talk, Paul referenced Old Testament prophecy. Specifically, he quotes Jesus saying Paul needs to go to the Gentiles, "to open their eyes, so that they may turn from darkness to light and from the power of Satan to God, that they may receive forgiveness of sins and a place among those who are sanctified by faith in me" (Acts 26:18).

The prophecies describing Jesus as a light to the nations are found in Isaiah 42:6 and 60:3, but especially 49:6:

"It is too light a thing that you should be my servant to raise up the tribes of Jacob and to bring back the preserved of Israel; I will make you as a light for the nations, that my salvation may reach to the end of the earth."

Agrippa was born around AD 27 and didn't move to Judea until around AD 50. As the great-grandson of Herod the Great (Matthew 2:1–4), he has some Jewish blood, and he knows the Jewish culture and religion (Acts 26:2–3). He is in a room filled largely with Romans while Paul, a Jew the Sanhedrin considers apostate, confronts him. He can believe the prophecies, and he likely understands Paul's line of logic, but converting to Christianity is a step too far (Acts 26:28). As with many people, "the cares of the world and the deceitfulness of riches and the desires for other things enter in and choke the word" (Mark 4:19).