The title of an important official in the Roman province of Asia. We do not know exactly what their job was. Several Asiarchs were worried about Paul's safety during a silversmith's riot in Ephesus (Acts 19:31).
We do not know much else about Asiarchs. We do not know: what skills they needed for the job, how long they worked as Asiarchs, or what their exact duties were.
It is not clear why there were many Asiarchs in Ephesus during the riot or why they cared about Paul's safety. They might have been leaders of the "Commune of Asia." If so, their job was to support and protect the imperial cult (the worship of Rome and the emperor).
The Asiarchs mentioned in Acts did not seem to dislike Christianity. Christianity was challenging the popular pagan worship of Artemis (a Greek goddess).
The long story in Acts 19 shows one of Luke's main ideas: Christianity wasn't trying to cause trouble, and Paul was not a political threat. If he had been, the Asiarchs probably would not have helped him.