It is a needlecase or needle book made from fabric that folds up. Embroidery needles, etc. go through the fabric on the inside, and then it is folded up and tied. Fanny bought them from some 'emigrants'. The book Jane Austen: The World of Her Novels by Deirdre LeFaye shows a picture of one. In the book, she also notes that the reference to 'emigrant' is probably a remnant of the book originally being written in 1795 and that the emigrants in question would have been French ladies who fled to England to escape the French Revolution.

Here are a couple of links to some images I found online that resemble the one in the book:

huswife