Well it's all far from being as simple as it might seem. Suppose, for example, that Eve married two different chaps, Shem and Ham, say, and had one child from each liaison. And suppose that Shem and Ham were both sons of a chap called Noah, but with different mothers. Then Noah could have been the great grandaddy of us all, without ever having known, biblically or otherwise, Eve. And it gets worse.
Suppose Shem and Ham now marry two daughters of a woman called Lilith and go on to populate the world. Then Eve and Lilith would both have been the common ancestor of all of us, with little to choose between them and no way to tell who was first. By hypothesising selective breeding, we can produce as many potential Adams and Eves as we want.
Not African Adams and Mitochondrial Eves, however, for they are something special. The Eve in question was identified by comparing the DNA of her mitochondria (which swarm inside our every cell to play an essential role in the process of respiration) with that of other women from various parts of the world. Everyone's mitochondrial DNA is precisely, give or take a random mutation or two, that of their mother. Most of our genetic code is a scrambled mish-mash from both parents, but mitochondria travel down the female line. So Eve is not just our great-great-great... granny, she is our mother's mother's mother's... mother. The mother of all mothers, in fact. And African Adam, identified by a computer analysis of the men- only Y-chromosome, is everyone's father's father's father's ... father.
The curious thing, though, is that Adam may have lived long after Eve. Since men are liable to father more children than women, we would probably not have to go so far back to find an Adam who populated the world as a comparable Eve.
Mitochondrial Eve and African Adam may be uniquely the most recent people for which those properties can be claimed, but that is a long way from being the earliest common ancestors of all of us. Such universal grannies and grandads were almost certainly much more recent - probably numbered in thousands of years rather than many tens of thousands - and there would have been plenty of them to dispute the honour.