When the conductor is not connected to a circuit through a battery, the electrons inside the conductor are in random motion but when the conductor is connected to a battery, the electrons move in a specified direction. This shows that something causes the electron to move it in a specified direction.
When the ends of the conductor are connected to the terminals of a battery a uniform electric field is set up throughout the conductor. This field makes the electrons move in a specified direction. The electrons in a conductor move opposite to the direction of electric field.