Dictionary.com's definition of charisma: "2. a spiritual power or personal quality that gives an individual influence or authority over large numbers of people."
And since I seriously doubt that idols are dealing with spiritual powers. Unless we believe that Mikitty really is a goddess. In that case punish me, Miki-sama.
Charisma is, to me, the most important actor in an idol. While people go over singing skills, dancing skills, acting skills, personality and looks, all of those are second to the factor that is charisma. Charisma is simply the thing that sets apart an idol. All other flaws can be forgiven if a girl has serious charisma. Because it really is that "it" factor, the unknown thing that just makes someone interesting and appealing.
And the one idol I'd say has oodles of charisma...
AKB48's number 1 front girl, Maeda Atsuko.
Now first off, let me preface this by saying that while I like Acchan, she's not my favorite AKB girl. She's definitely not in my top 5 members and probably not in my top 10 AKB members. However, she has oodles of charisma.
Acchan's value as front girl of AKB48 is something that's been contended for quite some time. And it's somewhat fair. Acchan doesn't have the best singing voice, the best dancing skills, the best looks (though she is very pretty) the best acting skills, and while she has a sweet, girl-next-door type of personality she's not particular in that regard. Yet there's just something about Acchan that's compelling and hard to deny.
When I first got way into AKB, I was kind of anti-Acchan. Not TOO bad, but I'd definitely wonder what Acchan has that my favorites didn't. However, what Acchan really has is this great charisma that makes her successful.
I think every idol needs charisma, but it's Acchan that definitely has it.