Comment by Sprocklem

IIRC, both of these are more or less true:

> THE EN DASH IS ABOUT AS WIDE AS AN UPPERCASE N; THE EM DASH IS AS WIDE AS AN M.

> They’re called that because those are the specific typography jargon words that refer to the height of a physical piece of type (the “em,” also called the “mutton” to reduce confusion) and half that height (the “en,” also called the “nut”).

An em was traditionally the width of an uppercase M and an en half that (around the width of an uppercase N). Nowadays, this relationship doesn't necessarily hold: one em is equal to the font size (e.g., a 12 pt font has one em = 12 pt).