[InnocentB]

I think you're a bit confused here. It's the height of the capital M, not the width of the lowercase em, that is generally 1em.

[thisrod]

"In olden days, an 'em' was the width of an 'M', but this is no longer true; ems are simply arbitrary units that come with a font" - the TeXbook, p60

[LukeShu]

Yeah, it's the height now, but the name derives from the width of an "m", half an em is an "en" (as in em-dash or en-dash)