The DNA structure of a person can carry ancestral identity of a person. There are some features in your DNA that remain unique to your ancestry. DNA is the hereditary material that can show a link from one person to another therefore the ancestry can't be left out. See details at http://en.wikipedia.org/wiki/Genetic_genealogy#Uses.
Mitochondrial DNA is inherited solely through the mother, as opposed to nucleic DNA which is a combination of the DNA inherited by both the mother and father. The ancestral integrity of nucleic DNA would be a hopeless jumble through generations of people each contributing his or her own specific ancestral heritage. But the mitochondrial DNA would still be largely unchanged since the time of your ancestors.