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.
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.
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.
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.