The history about the pica pint is quite interesting (at least for me). And it has to do with the way we measure types.
In the beginning
From the early days of the emergence of the printing press, and the mythical Gutenberg and for a long time, each printer, each workshop had its own way of measuring the types used. Its own scale.
This scale was arbitrary and used certain grades or reference magnitudes that were quite quaint and with curious names, at least in the Spanish typographic tradition. In the English one I don't know, but the idea should not differ much.
Towards a standard measure
It was not until the eighteenth century when the matter began to be normalized. At the end of the first half of this century, a French printer named Pierre Simon Fournier (the younger) tried to normalize that mess by creating a unit of typographic measure: the point. What Fournier did was take the smallest grade and he divided it into six parts, so the sixth part was the point and eleven points formed a cicero.
Almost twenty years later, François-Ambroise Didot perfected the defining point system from a French measure of length called pied-du-Roi, where 12 points (12 was a common number for dividing things before the metric system) formed a cicero related now with the ancient French inch. Notice that curiously it is France that began to normalize and look for a more orderly system of rational measurement, which gave rise to the metric system, SI base.
And so the Didot point, which was the unit of typographic measure most popular in Europe until the second half of the twentieth century, except in England and its colonies, was established.
In the Anglo-Saxon world, the cicero had its counterpart, a unit of similar length called the pica, which in turn also divides into 12 parts called points. So far we have two types of points: pica points and Didot points. The Didot points were defined as the 1/144 part of the old French inch, meanwhile the pica point measures 1/72.27 of an inch. I honestly do not know to what that extra 0.27 is due, but in traditional English typographic practice that is the value that it has been for centuries.
Then came Knuth and there was light
Then the (western) world was divided into two for a long time; measurement systems were not compatible. It is in this part of the story when Donald Ervin Knuth who is, as we all know here (I think), among many other things, the author of TeX, which in turn is the basis of LaTeX, ConTeXt, etc. Knuth was born in Milwaukee, Wisconsin, where his father owned a small printing business where Knuth, since childhood, was familiar with the technique of composition with types, which years later will abstract to create TeX. In those years the traditional pica and pica point were not rounded.
Adobe conquers the world
In the second half of the twentieth century appeared computers, which in the 80s began to become popular and to enter into virtually all human activity, including typography. The 80s were the times of typographical democratization. They were also the days in which Adobe and PostScript emerged, and quickly spread throughout the world. Then came the war of the Desktop Publishing systems and everything else.
It was then, when from Adobe came the idea of simplifying the point, rounding it to 1/72, whereby a smallest point was obtained but it was fully compatible with the English inch. Opposition to this practical idea must have been very small, let alone considering Adobe's influence is such that it has been the market leader ever since. And that is the cause of the discrepancy in measurements between the TeX point and that used by Adobe products and software manufacturers that support the standard imposed by Adobe.
As you can see in egreg’s answer, The TeXbook is an earlier piece than the domination of Adobe and its rounded pica which is called also the PostScript pica. And that's why TeX works with traditional pica points. Because it was created by a man born inside that typographic tradition (and not the European) and it was a few years before the tradition changed. Currently the PostScript pica is used by almost everyone (even unknowingly), so that Didot points and other measurement systems are practically extinct.
Nevertheless TeX is able to work with all the units mentioned in this story.
dd Didot point: (1157 dd = 1238 pt)
cc cicero: (1cc = 12 dd)
pt Traditional pica point (and the default LaTeX unit)
pc Pica: (1 pc = 12 pt)
cm centimetre: (2.54 cm = 1 in)
mm millimetre: (10 mm = 1 cm)
in inch: (1 in = 72.27 pt)
bp big point or rounded point or PostScript point: (72 bp = 1 in)
sp scaled point: (65536 sp = 1 pt) The smallest length unit in
em quad, a space that is one
M letter wide
ex the height of an
x or the lower case letters.
These are the units that TeX supports that can be used in any document. More than what a Desktop Publishing System can withstand. As I remember, InDesign, e.g., can work with centimetres, millimetres, inches, picas and points, both PostScript and traditional, but I think not with ciceros or Didot points.