A bookbinding style where either the spine and corners, or the spine and fore edges of the cover are of a strong material, usually leather, while the middles of the boards are of weaker decorative material. Paper and cloth are the usual choices.
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cbustapeck points out that the corners and spine strip will vary in size depending on the binder's taste. Corners in particular can be as small as a centimeter on a side or so large that they all but obliterate the central material.
This is less expensive than a full binding, but affords more protection to the vulnerable fore edges and corners than a simple quarter binding. It became popular in the Victorian era, when the middle classes were obtaining libraries for the first time. Like quarter bindings, half bindings look the same as full bindings when lined up on a shelf - but cost much less to obtain.