A very simple circuit consist of a resistor, a battery, and some conducting wires connecting the resistor to the battery(assuming resistance of the conducting wire is $0$). It is always assumed that both the ends of the conducting wire, i.e. one connecting to battery's terminal and other connecting to the terminal of resistor, are at equal potential and hence the potential difference is zero.
If the potential difference is zero inside conducting wire, then it implies that electric field inside the conductor must be zero. If this is the case then why does an electron inside the conducting wire move, and why there is current flowing through the wire?
If the electric field inside conducting wire is zero then it only means that electrons inside conducting wire are not accelerating but can move with a constant speed and since current is the rate of flow of charge per unit time, so it is possible for electric current to exist in the conductor.