Under normal conditions, electrons do not move in a specific direction. They move randomly here and there.
However, when Electric Potential Difference is applied, the electrons start moving in the same direction and this produces electric current.
For example, consider a pipe with two open ends. It has some water in it. You are holding the pipe horizontally in the air such that water does not spill out. Now when you turn the pipe slightly to one side, a "difference" in height is created and the water starts moving towards the lower end. This is potential difference created to move water in a specific direction.
Similarly, Electric Potential Difference is created and then only electrons move in a specific direction.