When an electric current flows in a conductor, it flows as a drift of free electrons in the metal. Electricity flows easily through a conductor because the electrons are free to move around in the object. Whenever there is a movement of electrons through a conductor, an electric current is created.

Take a metal wire AB such that there are at the same potential (which may be 0 V or somewhat) and thus no electron (current) flows through the wire. Now suppose we connect the positive terminal of a cell/battery to end A of the wire and end B is at the negative terminal. Now, we can clearly observe that the two ends of the wire are at different potentials and there is a potential difference across them. As metals have a number of free electrons therefore these electrons will move from lower potential terminal to the higher potential terminal.It is because when the two ends of the circuit is connected to the battery then the battery generates an electric field in the wire. This electric field forces the free electrons to move toward the high potential (positive terminal) of the battery.This is how current flows.