Okay, Brooke McEldowney (he of Pibgorn and 9 Chickweed Lane fame) is one of my favorite cartoonists, but I don’t get the punchline in this one. That doesn’t matter, though, because I want to mention the references to apostrophes in the first cell. [I just figured out that it’s not “cell,” but “panel.” At least that’s what I see the cartoonists using, and they ought to know. Several panels make a strip, and a “cel” is a single frame in an animated movie. I guess a “cell” is where you put prisoners or honey.]
Okay, in the first panel, she mentions that apostrophes are to indicate a missing letter in a contraction, and separately to indicate the possessive case. As it happens, the possessive is also derived from a missing letter! We still see it in the German, whence we get a lot of our possessive forms. Originally the possessive was -es, and we took out the e and replaced it with an apostrophe.
My other comment is the pair of apostrophes in one word. You can actually do that, sometimes. For instance the helping verbs in the future perfect, “will have” can both be contracted, mainly in informal spoken English: “I’ll’ve been writing this blog for nine years come January.” If I think of (or see) any other examples, I’ll add them.
Meantime, if you get the joke, explain it to me.