This phrase comes from the beginning of The Emerald Tablet and embraces the entire system of traditional and modern magic which was inscribed upon the tablet in cryptic wording by Hermes Trismegistus. The significance of this phrase is that it is believed to hold the key to all mysteries. All systems of magic are claimed to function by this formula. "'That which is above is the same as that which is below'...Macrocosmos is the same as microcosmos. The universe is the same as God, God is the same as man, man is the same as the cell, the cell is the same as the atom, the atom is the same as...and so on, ad infinitum."

This message theorizes that man is the counterpart of God on earth; as God is man's counterpart in heaven. Therefore, it is a statement of an ancient belief that man's actions on earth parallel the actions of God in heaven. This pivots on the belief that "all things have their birth from this One Thing by adaptation."

To the magician the magical act, that of causing a transformation in a thing or things without any physical contact, is accomplished by an imaginative act accompanied by the will that the wanted change will occur. The magical act and imaginative act becomes one and the same. The magician knows with certainty that for the change to occur he must will it to happen and firmly believe it will happen. Here it may be noted that magic and religion are akin: both require belief that a miracle will occur.

To bring about such a change the magician uses the conception of "dynamic interconnectedness to describe the physical world as the sort of thing that imagination and desire can effect. The magician's world is an independent whole, a web of which no strand is autonomous. Mind and body, galaxy and atom, sensation and stimulus, are intimately bound. Witchcraft strongly imbues the view that all things are independent and interrelated." These concepts pivot on the belief that all things come from the One Thing, or First Cause, and "Its power is integrating, if it be turned into earth."

The purpose of all rituals in ceremonial magic is to unite the microcosm with the macrocosm to join God, or gods when invoked, with the human consciousness. When such a supreme union is achieved the subject and object becomes one. This is because the magician feels that he is consciously in touch with all elements of the universe, therefore, he can control them. It may be said, the magician feels connected with the universe. This feeling intensifies the more the magician successfully practices his skills. Whenever he experiences a failure he knows that the ritual was not performed correctly.

When feeling unison with the universe the magician knows he has reached his Higher or True Self because he has attained mastery of himself and the universe. Thus he feels his "skillful work ascends from earth to heaven and descends to earth again, and receives the power of the superiors and of the inferiors." Therefore, he "hast the glory of the whole worldtherefore let all obscurity flee from thee." Now the miracles are possible.

Some magicians, including Aleister Crowley, claimed that when the magician reaches this ultimate peak of altered consciousness the miracles are no longer important, the extreme goal becomes the direct union with God. 

Sources: 29, 45, 66.

http://www.themystica.com/mystica/articles/a/below_above.