The story is that this is a tear catcher or tear bottle, used to collect the tears of mourners in Persia (i.e. Iran and Afghanistan). According to tradition, bottles like this (and in other shapes and from other places) were used to catch the tears and the more tears the more regret over losing the loved one. The shape of the opening, theoretically, is meant to fit over the eye, although it doesn’t really fit very well and I can think of much better designs if that’s really what it’s about.
I’ve never been terribly comfortable believing that they were ever actually used for this, but that’s the story. I’ve never found any convincing proof that they were actually used for this purpose. Interestingly, the Wikipedia page on them has very inconclusive and even somewhat conflicting statements about them and most of the statements are tagged as needing a citation, so even those are pretty suspect (not to mention that nearly everything you find there is suspect).
I don’t think this bottle is terribly old. If it is, it’s in terrifically good shape. It is, however, a remarkably beautiful, cobalt blue and regardless of the veracity of it’s origin and original use, it’s a beautiful example of the glass blower’s art.