[losvedir]

I used to think "em" was defined as the width of the letter m (hence the name), but The Elements of Typographic Style doesn't mention that:

Type is usually measured in picas and points ... but horizontal spacing is measured in ems, and the em is a sliding measure. One em is a distance equal to the type size. In 6 point type, an em is 6 points; in 12 point it is 12 points ... Thus a one em space is proportionally the same in any size.

The book then shows a little diagram with several different sized squares.

So, as I understand it, one em is the width equal to the height of a font (which is generally, but not always, the width that the letter m is designed as). What your quote is saying, then, is all the letters fit in a box which is twice as tall as it is wide.

[stan_rogers]

There was a bit of a "redefinition" when digital typesetting came along. An em used to be an M-width (and only made sense as a width measurement, as it changed drastically depending on the letterface used at a given font size). But, then, there used to more than 72 points to the inch too.

[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)

[cormullion]

The meaning of the word 'em' changes depending on where you look for its definition. Typographers are very creative with things like units and standards: even 'point' has had many different meanings.