Jack told the Doctor he was the 'Face of Boe' but it was never explained how. So how is that possible or was he just exaggerating?

I don't think he was exactly exaggerating or lying. However, the "face of Boe" as a flattering pamagat for a model could be unrelated to the Face of Boe as the character we know. I doubt it though. madami likely, he'll get decapitated some time in future, and possibly his body would grow a new head, but his old head would be preserved and would remain conscious, eventually developing into the Face of Boe.

To be honest, I kind of attributed this to the old myth that our ears and noses keep growing as we age while the rest of our bodies shrink. The idea being that if a human was technically immortal and yet continues to age, after a long enough time had passed, that person would be nothing BUT nose and ears. lol

That is apparently a myth, but hey. It's Doctor Who, not Doctor Oz. :)