In sexually reproducing organisms, mitochondria are normally inherited exclusively from the mother. The fact that mitochondrial DNA is maternally inherited enables researchers to trace maternal lineage far back in time.
Mitochondrial Eve (mt-mrca) is the name given by researchers to the woman who is defined as the matrilineal most recent common ancestor (MRCA) for all currently living humans. Passed down from mother to offspring, her mitochondrial DNA (mtDNA) is now found in all living humans: every mtDNA in every living person is derived from hers. Mitochondrial Eve is the female counterpart of Y-chromosomal Adam, the patrilineal most recent common ancestor, although they lived at different times.
She is believed to have lived about 140,000 years ago in what is now Ethiopia, Kenya or Tanzania. The time she lived is calculated based on the molecular clock technique of correlating elapsed time with observed genetic drift.
Mitochondrial Eve is the most recent common ancestor (MRCA) of all humans via the mitochondrial DNA pathway, not the unqualified MRCA of all humanity. All living humans can trace their ancestry back to the MRCA via at least one of their parents, but Mitochondrial Eve is defined via the maternal line. Therefore, she necessarily lived at least as long, though likely much longer, ago than the MRCA of all humanity.
Mitochondrial Eve is a person who is a common ancestor to all living humans on a female-only ancestral line. The fact that such a person existed is a logical consequence of the two facts: that humans are one species; and that no one has more than one (biological) mother. It should be stressed that “Eve” is an abstraction: as the most recent matrilineal common ancestor of living humans, it is possible for her identity to change, though it would now be necessary to kill off a large proportion of the human race in order to achieve this.