Of course, this will be an evolving document, and we welcome your input to help improve the FAQ and to keep it timely. Crystal sets help us to understand the technical history of the 20th century. In very early commercial radio, crystal sets provided inexpensive receivers that allowed a large listening market to develop. During World War II, improved crystal diodes made British and American radar receivers more sensitive than German models. Crystal diode research provided materials and techniques used in the invention of the transistor.
Crystal sets provide a step-wise introduction to electronics.
Most beginner crystal sets need only an antenna, ground, coil, capacitor, diode or crystal and headphones. Many modern electronic systems still contain crystal set-like circuits. Each of these definitions will bring up new questions and, as Lawrence says, more interesting questions. For instance, understanding a capacitor requires understanding conductors, insulators, electric charge, electric fields and how energy is stored in an electric field. You might need 5 new definitions.