Anything immemorial is very, very old. You're most likely to hear this word in the phrase "time immemorial," a common way to say "so long ago that no one remembers it."
The French immémorial means "old beyond memory," from a Latin root. Don't confuse this adjective with immemorable, which is sometimes used instead, but which literally means "not worth remembering." Immemorial is a perfect way to describe ancient things, including stories, customs, religions, and even time itself.