How do charges move through an insulated wire connected across a battery? use the terms potential difference, current, conductor, and insulator in answer.

Battery is the source of electrical energy which will help the charge to flow through a medium.

Battery is a constant source of potential difference which will create constant potential difference across the ends of a conductor where it is connected.

When a charge is passed through the constant potential difference then the change in electrostatic potential energy will give kinetic energy to the charge.

It is given as

so here charge will continuously flow through the conductor across which potential difference is applied by the battery. This constant motion or flow of charge is known as electric current.