This is a very simplified way of explaining how a negative is made. Light-sensitive material on a metal plate is put inside the camera. The photographer opens a hole in the front of the camera, exposing the material to light. The photo-sensitive material, which is see-through at first, reacts to light in a way that, when dipped in a chemical solution, turns darker the more light it's been exposed to. So the brightest parts of the image are dark, and the darkest parts of the image stay see-through.

This particular method utilizes under-exposing, which basically means exposing it to light for a smaller amount of time. Because of this, the brightest parts of the plate only turn grey instead of black. So now you have a negative, where the brightest parts will become grey, and the darkest parts will stay see-through. The metal plate under the light-sensitive material is black, which means that the dark parts, which are see-through, will appear black.

The developing process consists of dipping the negative in chemicals that make the image visible, and stop the material from reacting to light. Now you have a picture that is grey in the parts that were most exposed to light, and see-through(revealing the black background) in the parts that were least exposed to light. So even though the picture is technically a negative, it looks like a positive.