One of the most difficult aspects of paper cutting for me is still trying to decide and/or determine what I am going to cut. I still get confused sometimes and it often happens that I end up with the exact opposite of what I wanted. The problem is a visual or spatial one but most artists know it as positive vs negative space. While I have never taken an art class, I will try and explain it as best as I can.
In paper cutting, when you cut away all of the material that you don't need and are left with what you want then you are working with the positive space. In the image above, you are working with positive space. In other words, I would cut out all of the paper around the stool and would be left with a cutout of the stool (the image in black).
When you work with the negative space, you cut out the material that represents the image that you need/want. In other words, you make a stencil. In the image above, the negative space would be the white space.
To complicate the matter, if you spray paint the negative then you end up with the positive.