Negative space is how we describe the areas of a picture that you aren't drawing. So, if you are drawing a chair, the negative spaces are the shapes between the rungs, and all the space around the chair. Why is this important in drawing? Negative spaces often form useful shapes that you can check to determine if your drawing is in proportion. To do a negative-space drawing correctly, you need to draw the negative-space shapes, and ideally any detail within them, carefully placing them on the page so that they all add up to reveal the positive space taken up by the object.
Details can be drawn in, or they can be left as shaded spaces to give a silhouette. Either is correct, so long as the focus is on the small shapes between the parts of the foreground object, not on the outlines of the object itself.
The correct approach to negative-space drawing focuses on creating the shapes between objects or parts of an object. When talking about negative space, most drawing books will show you an example where the outline of the object is drawn and the negative spaces are shaded in. This may result in a silhouette, but this is not negative-space drawing. Sure, the shaded areas are indeed the negative spaces, but you haven't drawn them. You've drawn the positive ones, focusing on the outline of the object.
A negative-space drawing in progress
An example of an incorrect approach to negative space