Common term for the covers of a hardbound book. The term 'boards' refers to the thick cardboard under the paper or cloth covering on the outside of the book. The cardbaord manufactured and used for that specific purpose is called binder's board.
Some of the earliest forms of bound books would have used actual wooden boards, often covered with leather, sewn over the pages of the text. Vellum or parchment pages were reactive to changes in humidity, causing the potential for the pages to not lay flat as they reacted to their environment. Heavy wooden coverings on the book would help keep the pages flat.
As book binding transitioned to the use of paper instead of animal skin, the need for heavy wooden boards was reduced, so publishers would use a pasteboard or cardboard covered with leather or cloth in place of wood.