A type of bookbinding that combines the strength of a sewn hardcover book with the light weight and flexibility of a paperback. Essentially, it is a paperback book with a sewn binding. Books bound in this fashion generally look the same as normal paperbacks, except that when one looks at the top edge, one sees a signature sewn binding, not a perfect binding.
The most common sort of sewn softcover is a flexible binding. The signatures are sewn together, then a heavy layer of flexible glue is put on the spine. This is necessary as the thread alone does not have the strength to hold the binding together under moderate to heavy use. Additionally, it holds the book to the cover, the same sort of wraps that are used in normal paperbacks. The cover provides the same sort of support and rigidity that tapes or cords would provide in a sewn hardcover binding.
Less common is a style of sewn softcover that is essentially the same as a sewn hollow back hardcover, except that instead of stiff boards, light cardstock is used. This stock is usually slightly heavier than a normal paperback, and never (that I have seen) covered with any additional paper or cloth.
Some publishers, most notably Taschen are now publishing a sort of sewn softcover that is essentially the same as a hardcover, but with paperback type wraps. The bindings are sewn and pasted to the wraps. A hollow back binding is used. The lightweight boards are covered with an additional layer of printed paper (instead of the usual cloth or leather) and the endpapers are pasted down. They cost a bit less than a harcover of similar size would cost, and are much easier to handle.
Sewn softcover bindings are generally used on books that will receive heavier than normal use - classics, some reference books, textbooks, as well as many art books. They take up less shelf space (no boards) but are often heavier than hardcover books, because the book block weighs more per volume than the boards. The high flexiblilty is especially useful in long books printed on heavy stock (note many of the nice thousand page plus art and design reference works printed by Taschen), which are simply not suited to a hardcover format, due to the stress placed on the binding.
Sewn softcover bindings are confined almost exclusively to commercial publishers, as individual bookbinders who take the time to sew a binding generally want to put a sturdier covering on their work. They are easier for individual bookbinders to tear down and rebind, as the heavy layer of glue on the spine peels off relatively easily.
This method costs more than a perfect bound book, but less than a sewn hardcover. It is generally cheaper to do in a small edition than a sewn hardcover.
This method of binding has gained considerably popularity in the US in the past 20 years. Evilrooster offered the following: "There were some sewn softcover books in the early twentieth century as well - Penguin in particular produced sewn softcovers into the Thirties, only gradually changing over to perfect bindings. I have a couple lying around that I may rebind sometime." Sewn softcover bindings were also seen on many French and Italian books, starting at the beginning of the twentieth century, usually coupled with very high acid paper.
Overall, a sewn softcover is a really nice compromise in price and quality between a perfect bound softcover and a signature sewn hardcover, and definitely a better value than a perfect bound hardcover.