Vestigial structures support the theory of evolution by adding observable evidence to the model of common ancestry. Vestigial structures are not necessarily without function. In fact, according to Austin Cline at About.com, it isn't possible to demonstrate that any anatomical feature serves no purpose. Instead, a vestigial structure is one that shows clear homology with a similar feature in related organisms but whose purpose is no longer clear.
One example of a vestigial structure demonstrating common descent is the pelvic bones of modern whales. This bone girdle serves as an attachment point for the legs of terrestrial mammals, reptiles and other air-breathing vertebrates. The pelvis was a common solution to the challenge of walking against gravity on land. Fish do not have pelvic bones, as their environment is governed by buoyancy rather than gravity. Whales live in the same environment as fish, and they do not have terrestrial legs, but they do retain a tetrapod-style pelvis in the same location as their land-dwelling ancestors. While the pelvic girdle of the whale serves as the attachment point for several muscles, it shares a common structure with the homologous bones in land-dwelling species. Evolutionists attribute this similarity to whales and other tetrapods having descended from a common ancestor that had a pelvis of its own.