Vestigial structures are those structures that are present in a species, but that have lost most or all of their original functionality due to evolution.An example would be the wings of a flightless bird like an ostrich. In humans, the coccyx, or tailbone, is a vestigial structure.
Vestiges are considered to be evidence of evolution and are useful indicators of shared ancestry between different groups. Sometimes a vestigial structure will be transformed over time and put to a new use; additionally, sometimes we discover that a structure that w had thought was vestigial has a function, after all - the best example of that being the appendix, which is now believed to be important in reestablishing the normal gut flora after an illness.
Vestiges can also occur in behaviors and biochemical pathways, as well as structurally.