Reading through a few questions (this one in particular) I came across this quote:
Is Aunt Petunia a Squib?
J. K. Rowling: Good question. No, she is not, but — [Laughter]. No, she is not a Squib. She is a Muggle, but — [Laughter]. You will have to read the other books. You might have got the impression that there is a little bit more to Aunt Petunia than meets the eye, and you will find out what it is. She is not a Squib, although that is a very good guess.
We all know Petunia isn't a squib, she'd have to be related to James to qualify for that title. Ignoring logic where squibs and muggles and muggle-born witches become an issue, what could JKR possibly be alluding to?
Apparently the question was hilarious, and nearly killed her. I have searched around at least a reasonable amount and I have no idea what about Aunt Petunia is more than meets the eye. It would seem that there is exactly as much to Aunt Petunia as directly meets the eye, she's Harry's aunt, that's all.
Apparently I haven't "found out what it is". Can anyone enlighten me?