It could have happened several ways.  This is from the help center:

I got two requests for the same book!

This happens for one of three reasons:

• You Posted the book twice

  • using different ISBNs
  • or posted one or both copies as a non-ISBN item
  • or posted the same ISBN again after accepting a request for the first one you posted.
  • If you used two different ISBNs (or one ISBN and one non-ISBN listing), you should accept the request for the correct listing. If you posted the same ISBN twice, you should complete the first request and decline/cancel the second if you do not have two copies of the book.

• Two copies of the book were posted simultaneously when you posted the book.

  • This can be caused by a server hiccup OR by your clicking "Post book" or "Refresh" while the book-posting was in process.

• The requestor submitted two simultaneous requests

  • This usually happens when the requestor clicks again to request the book when the Request button reads "processing..."

It does not matter if the requestor submitted the request twice, or the book was posted to your bookshelf twice; the next step is the same, to correct the duplicate requests in your account, as follows:

If this happens:

• You can simply accept one request, and decline the other by clicking
  • When you decline, the extra book will be removed from your bookshelf.
  • Be sure you accept the request for the book that was listed correctly, if you listed it twice.

If the book is on a WIsh List and involved in a pending offer:

• Wait for the book to be requested. 
• Accept the first request
• Decline any extra requests by clicking
• Doing this will remove the extra copies from your account. 
• You will have a chance to explain what happened to the requestor when you decline a request.

The member is saying there was a system glitch and they received a request for a book they'd already mailed. I've seen a few reports of this glitch in the forums recently - books that had already been requested and sent and books that people had never had being requested. Not a big deal, they obviously can't sent you the book since they no longer have it so put the transaction behind you and move on, hopefully there is another copy or another on becomes available soon.

A couple of times now I have posted a WL book and had it show twice under WL holds. One time it was to 2 different people another time it showed up twice for hte same wisher. It's been a long time since it happened to me, but stuff like that does happen.

I had it happen to me two times, both times when I took my account off vacation hold. In one case, there were six wishlisted books that were double-posted, and in the other case, 3 books I had sent out months earlier and had been received re-appeared on my shelf when I took it off hold. Both of those incidents happened 2-3 years ago though and I haven't had any problems like it since, but weird glitches like that do happen from time to time.

Cheryl

Just tonight, I had a Live Help question about this very situation.  Member received a request last week, mailed the book and tonight she received another request for the same book and she had to cancel because she obviously didn't have the book.  Odd.