Understanding DNA supercoiling
It means that the direction in which the normal double-strand is wound up (which is also helical) and the direction on which the double helix itself is twited to reach the supercoils are opposite to each other. Have a look at this image from the Wikipedia, I think it makes this clearer:



The first show a DNA ring with the normal helix-coiling. The second show the supercoiling of the coiled ring molecule. Imagine a rubber band. This you can twist around its band axis to get the coiling and around its vertical axis to get the supercoiling.

For linear DNA molecules, this looks like this (taken from here):