If something has positive shape, negative shape will be present too. Negative shape or space is the space around the line(s) or shape(s)--i.e. the subject matter. The positive shape(s) will be the subject of the art, and the negative space(s) will be the part starting at the outside edges of the subject and extending to the edges of the paper or the edge of another subject. Negative shape plays just as important role as positive shape. Negative shape helps maintain good composition, harmony, balance and flow. Too much positive shape and the art will look crowded and too little positive shape and the art will look empty.
Negative space is important to consider especially when using mediums that do not have a white option (watercolor, graphite, charcoal, etc). Since the artist cannot add white later, she needs to make sure to plan out the white spaces beforehand and draw or paint around those spaces.
In the spatula example below, the negative space is the holes in the spatula and the entire area around the outside edge (we should have chalked all the entire sidewalk that wasn't the spatula). Notice that we didn't draw an outline around the edge of the shadow, we colored around it freehand. In the tree example, you can see where we filled in the negative shapes between the leaves.
As always, share what you discover with the class!