Bookbinding - A narrow strip of material (often cord or cane) covered in coloured stitching at the head and tail of the spine of a book. Headbands are only applied to books with a square, usually hardcovers.
spine
_____________
/ ___________ \
|\ OXOXOXOXOXO /| <- headband
|/ / / /|\ \ \ \|
/ / / / | \ \ \ \
/ / / / | \ \ \ \
A headband has a couple of functions in book structure. First, it protects the top and bottom of the spine, where the folded pages are susceptible to damage. Second, it reinforces the top and bottom of the spine covering, reducing the damage of repeated fingers hooking into the top of the spine to pull a book off of a shelf.
Headbands also have a decorative function, serving as a bright band to punctuate the shape of the book block. They lend distinction to a binding. The most traditional colour combinations are claret/white and blue/gold, but any combination may be used (often with no reference to the colour scheme of the book as a whole). Double headbands are occasionally used, for elaborate, or elaborate-seeming, bindings.
Originally, headbands were constructed directly on the book. Fine bindings still use sewn headbands. In the 1800s, the demand for more and cheaper books led to the use of pre-made headbands. Some bookbinders used any striped material available - even shirt fabric. The Bowden process, patented in 1855, however, created inexpensive, attractive headbands for mass market binding. It is still in use today to make header tapes.
An alternative to headbands are headcaps, which protect the head and tail of the book with an additional fold of the spine leather glued round a cord.