Every cell of our body has two different kind of DNA: nuclear and mitochondrial. The nuclear DNA is found in the nucleus of the cell, and is inherited from both parents. However, the mitochondrial DNA, which is inside the mitochondria, is inherited only from the mother. This is because when the spermatozoon fertilizes the ovum, it loses its tail, and only the nucleus of the cell is present, while the ovum preserves its organelles, such as mitochondria. So every mitochondria in our body is inherited from our mothers, who inherited from their mothers, and so on and so forth. When a woman doesn’t have daughters, her mitochondrial DNA is not transmitted, and her line is considered broken.
The name Mitochondrial Eve refers to the matrilineal most recent common ancestor, in an unbroken maternal line, of all currently living humans, who is estimated to have lived approximately 100,000–200,000 years ago. This doesn’t mean this woman (Mitochondrial Eve) was ‘the mother’ of all living humans today, or that she was 'the first woman'. It means that, in an unbroken line, she is the most recent woman from whom all living humans today descend.