An indelible pencil is a pencil with a type of lead which cannot be erased. Classically, indelible pencils are made with silver nitrate, although other materials may be used as well, and sometimes graphite is mixed into the lead for a familiar look and feel. A closely related pencil, the copying pencil, is a form of indelible pencil with an aniline dye embedded in the lead.
Indelible pencils were introduced in the early 1800s, as an alternative to the cumbersome and sometimes expensive pens of the era. Prior to the introduction of the indelible pencil, documents with any sense of permanence had to be written with fountain or quill pens. Indelible pencils created the desired lasting print, without the associated difficulties; markings made in indelible pencil would stay put if someone tried to erase the document, or if it was dropped into water or a solvent.
In the mid-1800s, pencil companies expanded on the concept of the indelible pencil to produce the copying pencil. Copying pencils have an interesting characteristic: when exposed to water, the aniline dye dissolves, creating a purple ink. Someone who wanted to be able to produce a copy of a document could write the document out with a copying pencil, and then blot the document with a moist piece of paper, creating a mirror-image copy. Typically, thin paper or tissue was used so that the writing could be read through the paper.
With the rise of the ballpoint pen and other cheap permanent marking alternatives, indelible pencils are not as common as they once were, but they are still available. Some artists like to work with them, for example, because they don't smudge, and they may also be used to mark things which could be damaged or compromised with ink pens. Art supply stores are a good source for indelible pencils, and these pencils can also sometimes be found at hardware stores.
Indelible pencils are typically clearly marked, to avoid confusion. You can also identify an indelible pencil by the fact that it lacks an eraser on the end, as the marks left by these pencils cannot be erased. However, it's a good idea to keep indelible and regular pencils separate, to avoid unfortunate mistakes.