My first encounter with a D&D sorcerer class was 3E. The 3E PHB says on p51:
Sorcerers create magic the way a poet creates poems, with inborn talent honed by practice. They have no books, no mentors, no theories -- just raw power that they direct at will.
In religious studies, "charisma" sometimes refers to the inner personal power in an individual, divinely conferred. I had to read endless writings about it in college, especially Max Weber, who described it as:
Charisma is a certain quality of a individual by virtue of which he is set apart from ordinary men and treated as endowed with supernatural, superhuman, or at least specifically exceptional powers or qualities. These ... are not accessible to the ordinary person, but are regarded as of divine origin or as exemplary, and on the basis of them the individual concerned is treated as a leader.
This is the aspect of Charisma often underplayed. (Also, I am not suggesting that anybody involved in writing D&D had to have read Weber, only that he's a good source for reading about this aspect of it.)
Charisma isn't just good looks or even greatness of personality. There is a sense of transcendent greatness about highly charismatic people.
You'll find more references to this sort of meaning of Charisma on the Wikipedia page for Charisma.