Scientists showed this through tests on what is called mitochondrial DNA, which is DNA found, outside the nucleus of a cell, in tiny organelles called mitochondria. We inherit our nucleic DNA (DNA in the nucleus of the cell) from both parents, but we inherit our mitochondrial DNA from our mothers alone.
It is possible to map the relationships between people through their mothers using mitochondrial DNA. When scientists examined DNA samples from people all over the world, they concluded that the whole human race descended from a single woman who became known as "the scientific Eve."
The scientific Eve may or may not be the biblical Eve. That we may all be descended from her does not prove she is the biblical Eve because, as Christians acknowledge, there may be more than one woman from whom we are all descended (for example, if the Deluge was universal, not local, then everyone is descended from Noah's wife).
Though science has not been able to confirm that its Eve is the biblical Eve, it has confirmed two important pieces of biblical revelation which many scientists used to deny. The first is that there was a woman from whom we are all descended, and the second is that there was a human pair from whom we are all descended.
This is implied by the former because we would all be descended from the scientific Eve and her husband, or, if she had more than one husband over the course of her life, we at least would all descend from the scientific Eve's mother and father. Either way, there is a human couple from whom we all sprang. Not only was there a scientific Eve, but a scientific Adam as well.