Lightning rods are constructed of a high-conductivity material with high current-handling properties, connected to ground. They work by being physically located usually higher than surrounding stuctures to offer a more conducive low-resistance path to ground for atmospheric "static electricity" charges, providing an alternative to surrounding structures becoming the discharge path to ground. When electrical charge differential builds up between earth and atmosphere to a sufficient point that particles in the air no longer act as an insulator - the particles "break down" providing a path for the discharge of the electrical differential ("lightning"). The lightning rod serves as an extension of ground placed above other potential condutive or semi-conductive materials (trees, buildings, whatever is desired to be protected from lightning), in hopes that the lightning rod will serve as the primary current path for the discharge rather than the structures desired to be protected. Every material will conduct electricity if the voltage differential across it becomes high enough. Things that readily conduct electricity (metal, water, etc.) have lots of "free electrons in their atomic structure and are called conductors (low resistance to current flow). They "give up" their electrons freely. Things that do not readily conduct electricity (glass, plastic, silica, salt, etc.) have few or no "free electrons" and are called insulators (or high-resistance to current flow). Materials with atomic structures that have some "free electrons" (in between those of good conductors and good insulators) are called semi-conductors and resist current (electron) flow until the charge across the material is moderately high. Electrical current, like water current, will always flow through the path of least resistance. A lightning rod works similar to a spillway at a dam, providing a path for the water to go before it builds up sufficient pressure behind the dam to break or crest over the dam. The lightning rod similarly provides a ready path to relieve the electrical "pressure" (voltage differential) before the resistance of the house, barn, whatever, "breaks down" and becomes the discharge path instead. Hope this helps..

In addition to Steeley's great answer. It is important to know that lightning rods that are mounted on the tops of buildings are placed there intentionaly to attract the lighning away from the more flammable building materials. At the bottom of the rod is attached a thick wire which is then guided across the roof and down the outside wall of the building but held away from the building by insulators similar to those you see on top of power line poles. When lightning strikes the rod (which is also insulated from the building), it finds it's "path of least resistance" through the wire, to the ground. When this happens the tremendous heat from the lighting evaporates the wire. Therefore, the wire needs to be replaced each time the rod is hit. If your barn gets het twice in the same storm, you'd better not be in it. If you think lighting doesn't strike twice in the same place, don't try to tell the owner of this barn: http://www.dalejtravis.com/barnpic/htm/00676.htm

In addition to Steeley & cmerch19602006's answers, lightning rods also help to draw off the excess atmospheric electrical charge before the charge differential can build up to the point of creating lightning. So, lightning rods can actually prevent lighting from actually striking in their vicinity.