What is (are) the medium of conduction for an electrical current with an external source in the human body?
Electric current flows rather rather easily through water that contains ions, which are electrically charged atoms. Since the human body is more than half water, and that water is filled with ions such as sodium, chlorine, potassium, etc., the body for the most part conducts electricity rather well.  The skin can have a high resistance to the flow of electricity, but it varies substantially, particularly being reduced when the skin is moist.  Medical electrodes, as for heatbeat measurements, are typically applied with conductive paste to overcome most of the skin's resistance.  You may want to look at this "Electricity And Human Body" page, or the article "Conduction of Electrical Current to and Through the Human Body: A Review".