This explanation looks likely:

"Well, we can look into this by examining the history of the apostrophe.  It is named after the Greek word apostrophos "of turning away, or elision".  So apostrophe was the elision of a letter or letters in a word.  That usage dates in writing from about 1611.  Interestingly, it was earlier that the punctuation mark apostrophe came to be so named as it represented the letters elided.  Shakespeare first uses the word in this sense in 1588 in Love's Labour Lost.  It is possible that the word for the process preceded the word for the punctuation mark but didn't make it into the written record.  English took the word from French apostrophe, which came from the Greek via Latin apostrophus.  


Keep in mind [there'll be a short test, later] that this apostrophe is a bit different from the poetic device known as apostrophe, in which a thing, place, or deceased person is addressed as though it can understand what is being said.  A good example comes from Wordsworth: "Milton! thou shouldst be living at this hour: England hath need of thee."


While we're on the subject, we should mention that the apostrophe used to denote possession is the same as the one described above that is used to denote a missing letter or letters.  How, you ask?  Well, the apostrophe in a word like fox's represents what was originally an e as in foxes.  So, before the apostrophe was adopted, a possessive was formed just like a plural: "Look at the foxes beautiful tail."  The use of the apostrophe for the e was then expanded to all words in order to denote possession.  This became widespread after 1725."

Regards,

A