Pastel is one of the mediums that artists use. Pastels are made up of colored power that has been mixed with a fixative such as Gum Arabic. The combination of ingredients is then put into molds that, when dry, produce small sticks that break easily. When the sticks are rubbed on paper, they deteriorate, leaving the powder on the paper.
Pastels are not the best medium because they have a tendency to smudge and fall off the paper. Soft pastels are able to imitate painting with oil paint or some other medium, especially when the whole paper is covered with a layer of pastel. In order to have an effect that is more like drawing, the pastels need to be harder and grittier like the chalk that is used on blackboards. The softer pastels were used by some masters like Latour or Chardin; the harder ones have more often been as a means of making studies rather than finished works.
Degas was extremely talented with his use of pastels, using them more for drawing than for painting. He would sometimes soak the paper in turpentine in order to have the color last longer. That is probably why many of his pastels are still in existence today.