I guess all photographers strive for this. We want to capture not the picture of you but "you". We want your image to reveal your soul. That serendipitous moment in time caught for posterity.
It's all about opportunity, that mixture of luck and preparation - an ineffable quality that might be akin to what all artists have: the knack to vicariously make a representation of reality, albeit real or abstract, the representation is "the look"
Maybe my lens' critical eye does this automatically? It should, considering how much I paid for it.
But whatever the answer, I like it when I can catch it.