There are roughly 72 points to an inch (more precisely 0·9962"). (In Desk Top Publishing software you can choose this traditional point or one of precisely 72 points to the inch). Twelve points, still referred to by the old name of "pica", is a unit used for measuring the lengths of lines of type.
Until the adoption of a point system types had borne no precise mathematical relationship to one another, nor did the sizes of one typefounder necessarily agree with the sizes of another. The different sizes were given names: Agate, Diamond, Ruby, Brevier, Canon, Great Primer - but since there was variation from one typefounder to another a rational system was needed to standardise the sizes for all.
A point system was developed in France in the eighteenth century but it was not until 1886 that American typefounders nominated a committee to consider the point system, and in 1898 the point system was adopted in England. The French point was fixed as 1/144 (*1/100 or *0·01) of two French inches; hence 72 points to 1 French inch. (The Didot point, used on the Continent, was not the same as ours; the body chosen was larger than ours, being nearly 14pt in our units, and this was rated at twelve Didot points).
There is also the "em". This is the square of any body size -, it is correct to speak of 6 pt. ems, of a 10 pt. em, and so on - but if no size is referred to then the "em" meant is the 12 pt. ot Pica em. Half an "em" is known as an "en"; these words sounding so alike many printers refer to them as "mutton" and "nut" respectively.
Below the em and en there are other standard spaces; as fractions of the "em" they are: 1/3 em or "thick", 1/4 em or "middle" and 1/5 em or "thin"; there is also the "hair" space of 1/12 em.
The usual sizes of metal type stocked by a letterpress printer are
6, 8, 10, 12, 14, 18, 24, 30, 36, 42, 48, 60, and 72 pt.
(Adapted from "An Approach to Type by J.R.Biggs)