Generally, current means a flow of something from one place to another place. For example, water falling from a hill, river water moving from one place to another place, and ocean water moving from one place to another place are known as water currents. In a river and ocean, the water molecules moving from one place to another place will conducts current.
In a similar way, the electric charge carriers moving from one point to another point in a conductor or semiconductor will conducts electric current.