Negative space is a confusing expression. It is in fact a very positive artistic device used by painters and photographers and, in short, represents the space surrounding the subject and restricted by the frame or borders. It is much more than any space, though – it defines your subject, in many cases it provides a story, a meaning and shape.
A photo won’t work unless there is a balance between the subject (positive space) and the negative space. Negative space must not be messy or create confusion.
I will finish at these general remarks but give an example of badly used negative space. Can you see the little island coming out of the man’s head? This looks confusing to the viewer’s eye and spoils the whole impression.