Negative space is a compositional tool used in both two- and three-dimensional work. The simplest way to describe it is as: "space where other things are not present."
You might refer to Leonardo's The Last Supper for a good example. Of late, the negative space between Jesus (in the middle of the painting) and the person immediately to his right is causing quite a flap. This "vee"-shaped negative space is credited with hiding secrets, by some.
You could also refer to much of M.C. Escher's, Bridget Riley's, Victor Vassarely's or any other Op artist's work for intricate examples of negative space in action. In these, we are often left wondering what, exactly, is negative and what is positive as back- and foregrounds seem to flip before our eyes.
Incidentally, negative space has no "negative" connotation. It's actually a wonderful, if often neglected, design element. Properly used (as with Henry Moore's sculptures, or Zen brush paintings, or even your basic Rorschach test ink blots), it is just as important as what is there.
