Most commentators assume that refers to an Egyptian who claimed to be a prophet and led a revolt against the Romans. The only source for his existence that I'm aware of is Josephus, who refers to him in both Jewish Antiquities and The Jewish War:

"There came out of Egypt about this time to Jerusalem one that said he was a prophet, and advised the multitude of the common people to go along with him to the Mount of Olives, as it was called, which lay over against the city, and at the distance of five furlongs. He said further, that he would show them from hence how, at his command, the walls of Jerusalem would fall down; and he promised them that he would procure them an entrance into the city through those walls, when they were fallen down. Now when Felix was informed of these things, he ordered his soldiers to take their weapons, and came against them with a great number of horsemen and footmen from Jerusalem, and attacked the Egyptian and the people that were with him. He also slew four hundred of them, and took two hundred alive. But the Egyptian himself escaped out of the fight, but did not appear any more." -- Jewish Antiquities

"But there was an Egyptian false prophet that did the Jews more mischief than the former; for he was a cheat, and pretended to be a prophet also, and got together thirty thousand men that were deluded by him: these he led round about from the wilderness to the mount which was called the Mount of Olives, and was ready to break into Jerusalem by force from that place; and if he could but once conquer the Roman garrison, and the people, he intended to domineer over them by the assistance of those guards of his that were to break into the city with him. But Felix prevented his attempt, and met him with his Roman soldiers, while all the people assisted him in his attack upon them, insomuch that when it came to a battle, the Egyptian ran away, with a few others, while the greatest part of those that were with him were either destroyed or taken alive; but the rest of the multitude were dispersed every one to their own homes, and there concealed themselves." -- The Jewish War

In the Bible verse you cite, Paul has been arrested for causing a disturbance in Jerusalem, so presumably the Tribune in question suspects he might be the same as the earlier troublemaker, who Josephus claims had disappeared after his movement was put down.