The Leyden jar is an early form of the electronic device now known as a capacitor and once known as a condenser. Its function is to store an electrical charge (or technically, a charge differential) for later release. The development of such a system was naturally of great interest to early experimenters with electricity, as it provided a practical and reliable way to bottle the object of their study.
A classical design for a Leyden jar follows. Begin with a glass jar. Coat the inner and outer surfaces either with metal foil or with a thin metal layer cast directly onto the glass. Cap the jar with an insulating lid transfixed by a metal rod. Connect the inner end of the rod to the jar's inner surface (with a metal chain, for example), and at the other end of the rod affix a convenient terminal such as a metal ball. Charge the jar by bringing the terminal into contact with an electrostatic generator (a Van de Graaff generator or one of its technological predecessors). Discharge the jar by connecting the terminal to the outer metal surface, by way of any creatures or apparatus involved in your experiment.
Using modern theories of electricty, we can abstract the construction of the Leyden jar very simply: it is a capacitor comprised of two coaxial cylindrical conductors separated by a glass dielectric. That the dielectric originally took the form of a jar was simply a matter of convenience, and was incidental to the function of the device. Very crude calculation using this model shows that one can easily attain capacitance on the order of 10-9 Farads (that is, nanoFarads).
The basic idea of the Leyden jar was conceived independently by Ewald von Kleist in 1745 and Pieter van Musschenbroek in 1746; the latter was more widely credited with the invention, to the point that it was named for his hometown of Leiden, Holland (the name was later
anglicized to Leyden). His original discovery involved a jar filled with water in lieu of a metal inner surface, and was discharged to earth ground rather than the local ground of an outer surface; the use of metal surfaces was advanced soon after, and significantly improved the jar's efficiency.
For verification, and additional electrical history, consider visiting the IEEE Virtual Museum at www.ieee-virtual-museum.org. Comments welcome. Thanks to ponder for settling the Leiden/Leyden point.