Albert Barnes Commentary Acts 16:39

"and they came and besought them; and when they had brought them out, they asked them to go away from the city." — Acts 16:39 (ASV)

And they came and besought them. A most humiliating act for Roman magistrates, but in this case, it was unavoidable. The apostles had them completely in their power and could easily bring about their disgrace and ruin. Probably, they pleaded with them by declaring them innocent and by affirming that they were ignorant that they were Roman citizens, and so on.

And desired them to depart, etc. Probably,

1. to save their own character and to prevent the apostles from taking any further steps to convict the magistrates of violating the laws.
2. to evade any further popular tumult on their account.

Paul and Silas chose to comply with this advice after they had seen and comforted the believers (Acts 16:40).

They had accomplished their main purpose in going to Philippi. They had preached the gospel, laid the foundation of a flourishing church (compare the Epistle to the Philippians), and were now prepared to carry their work into surrounding regions.

Thus, the opposition from the people and the magistrates at Philippi led to the founding of the church there; and in the same way, their unkind and inhospitable request for the apostles to depart was the means by which the gospel spread into adjacent regions.