What does Acts 23:15 mean?
Forty Jews have vowed to kill Paul as soon as possible and are asking the elders and chief priests for help. The text isn't clear who these Jews are. The term "the Jews" typically means religious leaders, but these assassins are going to the religious leaders for help (Acts 23:12–14). They may be Jews from the province of Asia in modern-day Turkey who accused Paul of bringing a Gentile into the temple (Acts 21:27).After these Jews accused Paul of desecrating the temple, a mob formed and nearly killed him. The Roman tribune heard about the riot and rescued Paul by arresting him. He asked the mob why they were attacking Paul, but most didn't know (Acts 21:27–36). Attempting to find out more, he allowed Paul to speak to the crowd, but that didn't help. He then tried to scourge the information out of Paul, but Paul's Roman citizenship protected him from torture before a proper conviction (Acts 22:1–29).
In a final effort, the tribune took Paul to the Sanhedrin to see if they could explain. Paul had his own agenda which included talking to the Sanhedrin about salvation through Jesus, but with only a few sentences he wound up insulting the high priest and turning the Pharisees and Sadducees against each other (Acts 23:1–10).
If the Sanhedrin promised to behave itself, it's very likely the tribune would welcome another chance to get these things straightened out. The assassins are also wise in implicating the Sanhedrin: they can devise a charge against Paul that justifies the act. This will prevent them from losing fellowship in the temple.
They don't know that Paul's nephew is listening. He reports the plot to Paul who sends him to the tribune. The tribune realizes there's nothing else he can do except keep Paul safe. He calls on two centurions to assemble a military escort to take Paul to the governor in Caesarea Maritima (Acts 23:16–24).