Negative space is the empty area around your subject, whereas the subject is the positive space. In this empty space, there is nothing of interest to see for your viewers, hence the eyes move towards the subject. There can be a lot of empty space, like in minimalism, what emphasizes your subject even more (that’s why minimalism is so powerful). But it could also be as equally spread as positive space. Such as in the product photo below. Just an empty white sheet to avoid any distractions from the product.
But there is more to negative space. It gives a sense of expectation. For example in pictures of the dog below on this page. The dog is looking intensely at something (being the photographer, I know it was a cat). Leaving a little empty space between the dog’s eyes and the edge of the photo, gives the viewers a change to wonder what he was looking at. If there was no negative space between the eyes of the dog and the edge of the photo (the picture on the right), the sense of expectation would have been gone. In these situations, try to position most of the negative space in the direction your subject is looking at.
Negative space is also very usable while capturing a moving subject. Try to keep (most of the) empty space in the direction your subject is moving to. Like the White Stork below. There is a lot of negative space in the direction the bird is flying to, adding to the sense of motion.
As shown above, keeping some uninteresting space around your subjects can be very useful, and contrary to “filling the frame” it makes you a viewer of the scene, rather than part of the scene. One last tip: negative space isn’t necessarily the sky or a white sheet. A wall or any subject will do.