If such a person existed, he probably lived between 35,000 and 90,000 years ago years ago, judging from molecular clock studies. While their descendants certainly became close intimates, Y-chromosomal Adam and mitochondrial Eve themselves never met: rather, they lived many thousands of years apart. They are named after the characters called "Adam" and "Eve" in Genesis, but should not be identified with them. Based on the DNA of peoples living in Africa today, both Y-chromosomal Adam and mitochondrial Eve are believed to have lived in Africa.
More on the process by which many lineages winnow down to one can be found in the article on mitochondrial Eve, which also elaborates on how Adam and Eve relate to the Out-of-Africa theory of human evolution.
See also: genetic drift -- molecular evolution -- Adam's Curse