History of Serif Typefaces
Serif typefaces originated from carvings in stone in Roman antiquity. The variation in thickness of the lines (or line contrast) and the angle that the thickness changes (the stress) comes from how the letters were carved in to the stone with a chisel.
From: A Typographic Workbook: A Primer to History, Techniques, and Artistry
By Kate Clair, Cynthia Busic-Snyder:
Angled or oblique stress in the letterform developed when a flat-tipped pen or chisel was held at an angle as the letter was drawn or carved. The thickest area of the stroke is the area of maximum stress[...]
Serif typefaces can be grouped in to a number of classifications that, amongst other things, have different stresses and line contrasts.
These typefaces date back to the beginning of the printing press and movable type. The contrast in thick and thin strokes is typically less than in later designed typefaces. Old style serif fonts have remained popular for setting body text because of their excellent readability on book paper.
The contrast of strokes in transitional serif typefaces was greater mainly due to the improvement of printing techniques developed in the 18th century
English printer and typographer John Baskerville established this style in the mid 18th century. [...] improved printing methods allowed much finer character strokes to be reproduced and subtler character shapes to be maintained. While the axis of curve strokes can be inclined in transitional designs, the strokes normally have a vertical stress. Weight contrast is more pronounced than in old style designs.
Modern (or Neoclassical & Didone) Serifs
The contrast in thin and thick strokes in Modern serifs is much more extreme and with a vertical stress. This typically makes Modern serifs less suited (although not unseen) for body text and were therefore some of the earliest 'Display' typefaces.
When first released, these typefaces were called “classical” designs. Early on, however, it became apparent to printers that these were not updated versions of classic type styles, but altogether new designs. As a result their classification name was changed to “modern.”
All Images and (unattributed) quotes from: fonts.com - Type Classifications