In this illusion, David Copperfield flies about the stage and than passes several tests to demonstrate that he is not suspended from wires. He has hoops passed around him and shows he can also fly inside of a covered glass box and while carrying a female volunteer.
John Gaughan, the creator of this amazing illusion, has revealed the method behind it. According to him, Copperfield is suported by wires. This wires are less than 1mm thick and therefore invisible to the audience. However, they can support 100kg each. They are mounted to a harness at Copperfield's hips. The harness is of course covered by the clothing.
Above the stage, the wires are attached to a computer-controlled rig that mantains the tension of each wire and moves the performer around.
They can all be easily explained. When the hoops are seemingly passed around him, they never really go above him, but are always twisted under him. It is an optical illusion. If you watch carefully, you can notice this at the first hoop demonstration.
When he floats inside of the glass box, the top of the box is threaded between the two sets of wires in a vertical position before being rotated ninety degrees and lowered into place. This way, the wires are passing through crevices between the lid and the slides. The "volunteer" was most likely a stooge.
For better understanding of the illusion, here is a video explanation with great computer stimulations of methods which were used: