A hardback is a book with a strong, stiff cover, not a soft paper one. You can hold it by the cover and it keeps its shape on a shelf. In Britain this is the usual word. In the United States the same book is usually called a hardcover — same object, different habit. Hardbacks cost more than paperbacks and last longer. Though actually, many books come out in hardback first, when the publisher still hopes to sell them as gifts or library copies, and a cheaper paperback follows later. You can say a hardback (the book itself) or a hardback edition. It is not “the hard back” of a chair, and it is not only the back cover: the whole book is a hardback.