What I've got here is David Crystal's story on the apostrophe: nowhere in his Encyclopedia of the English Language does he mention the hypothesis Dr Bill brought up; instead, he says it was introduced by 16th century printers simply as a way to indicate a missing letter. By the 18th century, as Brandon said, it became a marker for the possessive, first denoting the genitive singular, then the plural.

Crystal addresses the apostrophe in several different places in his wondrous work. I could quote chapters and verses, but it's got an index