What does Acts 21:37 mean?

The arrest which Holy Spirit has been warning Paul of is finally happening (Acts 20:22–23; 21:33). Jews from modern-day Turkey falsely accuse him of bringing a Gentile into the temple, and the Roman military outpost has him in chains. Paul doesn't seem to regard them as a mob of enraged Jews who want to kill him. He sees a group of lost souls who need Jesus. While he has them there, he wants to share his story (Acts 22:1–21).

First, he must convince the tribune to let him speak. For some reason, the tribune has Paul confused with someone else entirely.

Three years prior, according to ancient historian Josephus, an Egyptian huckster convinced a group of Jews that he could lead them into a battle that would expel the Roman overlords from Jerusalem. They camped at the Mount of Olives where he told the militia to wait until he commanded the walls to fall. They would then invade the Roman garrison, the Antonia Fortress, and take control of the city. Instead, Felix, the procurator of Judea, sent soldiers to the encampment where they killed or imprisoned several hundred of the would-be revolutionaries. According to Josephus, Jewish Antiquities, 20.8.6, the Egyptian quietly escaped. The tribune thinks Paul is that Egyptian. He's shocked when his "Egyptian" speaks to him in cultured Greek.

The barracks are the Antonia Fortress, the Roman military's outpost that houses 600 peace-keeping forces. The large building rises from the city level to above the northwest corner of the temple mount; from there, the guards can see much of the courtyard. Below and along the north wall of the mount are a courtyard and several smaller buildings. Herod the Great built it in 35 BC and named it after Marc Antony.