In typography, a bracket is a curve that connects the serif to the stroke. Popular, well-designed, bracketed fonts include Times New Roman, Caslon, and Garamond.

        |        |                         |        |                 
        |        |                         |        |                 
        |        |                         |        |                 
        |        |                         |        |                 
        |        |                         |        |                 
       /          \                        |        |                 
 +----`            `-----+          +------+        +-------+
 +-----------------------+          +-----------------------+
        bracketed                         unbracketed

When creating typography in stone, softer metal, or wood, brackets help structurally strengthen and stabilize the serif. For this reason, all early fonts were bracketed.

Brackets and the fashion of kings
Back when royalty cared about such things, in 1692 Louis XIII asked his Imprimerie Royale to reconceive typography on engineering and scientific principles rather than “merely” artistic ones. Among the committee's stylistic decisions toward meeting this goal (and it took years and heated debates) was the reduction of the bracket. Their ideal font, the Romain du Roi, became the height of fashion but protected for use strictly in royal printing. In fact it was a capital offense to use it otherwise. So other print houses around France tried to copy the Romain du Roi with just enough changes to keep their heads attached. The designers noticed the reduced bracket and exaggerated it, pushing the limits of hand-carvers’ precision and of metallurgy to hold the shape through printing. By 1702 a folio called the Médailles was printed that utilized a class of fonts that is now called transitional roman, and it completely lacked brackets.

Other, subsequent font classes that are, generally, bracketless include modern, slab-serif and of course sans-serif.

Now that we make most of our letterforms from bits, the presence of brackets is mostly a stylistic choice. Visually, brackets reduce the apparent contrast of serif-to-stroke, remove the visual “hot” spots caused by more precise angles, and feel less mechanical and more humanist. Most serifed fonts aimed at elegance adopt the bracket.