Negative space isn't the place your mind retreats to when a painting isn't going well. Negative space is the space between objects or parts of an object, or around it. Studying this can have a surprisingly positive effect on a painting.
In her book Drawing on the Right Hand Side of the Brain Betty Edwards uses a great Bugs Bunny analogy to explain the concept. Imagine Bugs Bunny speeding along and running through a door. What you'll see in the cartoon is a door with a bunny-shaped hole in it. What's left of the door is the negative space, that is the space around the object, in this case Bugs Bunny.
Is It a Vase or Two Faces?
The classic example is the brain-teaser where depending on how you look you see either a vase or two faces (as shown in the image above). It becomes very evident when the image is reversed.