There are many things for which we are without a full and understandable explanation. Sometimes we don't know the whole story. Sometimes the subject matter is beyond our understanding. The identity of this woman is a little of both. I believe that she represents a spiritual kingdom that influences and could be said to rule over the physical governments of the earth. It is an organization of people, but it is also demonic and satanic. It has existed for ages and has slowly increased in power until it has taken control of most (if not all) the governments of the earth.
The beast, the Antichrist, carries her. He supports her and uses her to further his purposes. The seven heads are the seven world-wide governments that she has operated through. The ten horns are the 10 kings of the whole earth who comprise one of these empires influenced by the woman, out of which the Antichrist comes.