The expression of course means not to know someone at all -- or te able to distinguish that person from any other person. The name "Adam" is from the Hebrew word "adam" meaning "man" (not man as opposed to woman but "man" as in "mankind" -- "I don't know him from any other person").
The best I can find on the origin of this use of Adam is this:
The form commonly used is 'not to know one from Adam's off ox,' meaning to have not the slightest information about the person indicated. The saying in any form, however, is another of the numerous ones commonly heard but of which no printed record has been found.
But in 1848 the author of a book on 'Nantucketisms' recorded a saying then in use on that island, 'Poor as God's off ox,' which, he said, meant very poor. It is possible that on the mainland 'Adam' was used as a euphemistic substitute. The off ox, in a yoke of oxen, is the one on the right of the team. Because it is the farthest from the driver it cannot be so well seen and may therefore get the worst of the footing. It is for that reason that 'off ox' has been used figuratively to designate a clumsy or awkward person.
In other words, the expression started out differently, with "God" rather than "Adam" as the term, and people who feel uncomfortable talking about "God" colloquially substituted "Adam."
I hope this helps.