Simply put, positive space is best described as the areas in a work of art that are the subjects, or areas of interest. Negative space is area around the subjects, or areas of interest.
Take a look at the image on the right.
For example, do you see faces or a vase?
If you are seeing a vase, then you are seeing the white area as the positive space. The black areas become the negative space. If you are seeing faces, then you are seeing the black areas as the positive space, and the white area as the negative space.