Like any exacting craftsman, a draftsman can be very particular about her tools. One encounters artists with extremely specific ideas about drawing basics such as which pencil is best, which paper will work, and even what eraser to use.
Today, most erasers are made of vulcanized rubber, which is latex-based. (People who are allergic to latex may find some latex-free "rubber" erasers in art-materials stores.) The most popular kind of eraser for artists is the kneaded eraser (also made of latex/rubber), which is usually gray and very pliable, allowing the eraser to last longer. It also melds back together and doesn't crumble, which allows an artist to keep the drawing surface neater and less prone to damage.
The first erasers (marketed in 1770 by an English engineer named Edward Nairne) were made of untreated rubber, which, as a natural product, dried out and otherwise deteriorated relatively quickly. Vulcanization, a process involving the heating of rubber along with a stabilizing element such as sulfur, made rubber more shelf stable.
Looking back further, drawers used the soft parts of bread to erase marks made by lead, graphite, chalk, and crayon. The notion is not so crazy--bread was readily available (except perhaps for the most starving of artists), and when it comes to erasing marks, the only important thing is strictly physical: The eraser component must be composed of molecules that are stickier than the molecules of the drawing surface so that the marking material is pulled away from the surface and adheres to the eraser.
On a related note, a Japanese manufacturer produces erasers that are in the shape of bread: