About.com explains that homologous structures are parts of organisms' anatomies that share a common origin in ancestral forms. These features' functions may be modified with time, but the structures are clearly related in gross anatomical detail. One example of animal homology is the common origin of the tetrapod upper-limb. This structure forms a front leg for most land-dwelling vertebrates, but it's an arm in humans and a wing in bats.
Though legs, arms and bat wings are all put to very different uses, each shares an underlying structure in common with the others, and it speaks clearly to their common origin. The human arm begins with a single bone, the humerus, which has a ball joint at the shoulder and a hinge joint at the end. There, it is joined to two smaller bones, the radius and ulna, which terminate at a wrist. From the wrist, five digits emerge. Bats' wings share the same configuration, though their fingers are longer and connected by skin. Horses' legs are also very similar, though they have lost all but one of the ancestral five toes.
Homologous structures are not to be confused with analogous structures, which share a function but not an evolutionary history. An example of this is the wing of a bat or bird and the wing of an insect. They perform the same function, but did not emerge from common ancestry.