This current is a motion of something. This question can be answered. Electric current is like a flow of syrup. Even maple syrup moves too fast, so that's not a good analogy. Electric current flows as slowly as a river of warm putty.
Energy flows fast, yet an electric current is a very slow flow.
The complicated answer Within all metals is a substance which can move. Calling it by this name can be misleading because charge is not energy, and the Sea of Charge exists within in all metal objects, all the time, even when the metal has not been made into a wire and is not part of an electric device. During an electric current, the wire stays still and the sea of charge flows along through it. When the flashlight switch is turned off and the lightbulb goes dark, the charge-sea stops moving forward. Even though it stops moving, the charge-sea is still inside of that wire.