What IS the Problem of Akrasia?

A little less than a month back, I delivered a talk, Aristotle, Anger, and Akrasia, down at Felician College -- discussing some material, and outlining certain issues, appearing in a book I'm currently writing, reconstructing Aristotle's theory of anger across the corpus of his texts.  I'd intended my next entry in this blog to use that as a starting point, continuing my on-again-off-again series on philosophical and theological treatments of anger (the last two, on Plato, are here and here).  Recently, a student from the University of Edinburgh -- who watched the video of the talk -- wrote me:
I came across your online lecture, which was very helpful, offering a very in depth description of the problem but you did not seem to offer a judgement on the problem itself.  Would you say that Aristotle effectively overcomes the problem of Akrasia?
So, that offers an excellent occasion for engaging in a bit of a digression in this post -- what precisely is the "problem of akrasia"?  -- that's what has to be asked, examined, and answered, before we can say whether Aristotle does or doesn't effectively formulate it, mainly in Nicomachean Ethics book 7, let alone overcome it.