Like many technical terms, this is a bit of a misnomer if you take it literally. Perfect binding is a bookbinding technique where, instead of being made up of sewn signatures, a book is created by gluing the back ends of all the pages into a block, using a flexible adhesive. Anyone who has had a cheap paperback start to shed pages like autumn leaves knows how "perfect" such a binding is.
Although the term "perfect binding" is modern, versions of the technique date back to the Victorian era. In 1836, William Hancock was granted a patent in England for caoutchouc bindings (named for his chosen adhesive, a kind of india rubber). Other, similar techniques were tried with gutta-percha.
There were good cost reasons to find a way around sewing the book block. The process is time-consuming, and troublesome to automate. With the rise of the middle classes in Britain, the demand for libraries was growing, and binders could not make books fast enough. Nouveau-riche clients, caring more for the gilt on the spines and covers of their books than the quality of the bindings, bought the new books by the yard. But the technique fell into disuse very quickly. The spines of caoutchouc bindings cracked with time and use, and the pages began to fall out of the cheap but shiny bindings.
Perfect binding was revived in the early Twentieth century, enabling the rise of the cheap paperback. Binders developed techniques to strengthen the book blocks by sawing small, angled grooves into the edges of the pages and laying cords or threads in them before gluing. However, the adhesives continued to fail. Customers minded less when a cheap paperback fell apart, but the technique was still far from perfect.
The real revolution came during and after World War II, as new adhesives were developed by the burgeoning chemical industry. Various forms of polyvinyl acetate, or PVA, are now commonly used in the publishing trade. Perfect-bound editions are a good way to sell mass-market books at prices affordable to virtually everyone. But the technique turns up in more expensive books as well, with much less justification. The hardcover edition of a new book is rarely sewn from signatures, and collectors' editions targeted at the mass market often enclose perfect-bound book blocks in gilt and leather covers.
You can tell a perfect-bound edition from a signature-sewn edition by looking at the spine end of the head or tail. If the pages make a series of U-shapes, you have a signature-bound book. If they do not, then your book is perfect bound.
Perfect bound books are not generally suitable for rebinding.