It's all the salts and impurities in it that cause it to carry current. Skin is actually a very good insulator as well so, relative to metal, humans aren't very good conductors. However, it is things such as the ionised water and whatnot that make up our body that do cause us to conduct (or)
A conductor is a material that allows electricity to flow through it. Some metals, the ground, and even water are good conductors. Add "your body" to that list, because human beings also conduct electricity. If an electrical current were to pass through your body, it would be an extremely unpleasant experience.