What is the summary on the back of a book called?

The summary on the back of a book is called a "synopsis." A synopsis sums up the plot of a written work, providing a brief description of the main events of the storyline. The plural of synopsis is "synopses."

The noun synopsis comes from Late Latin, originally from the Ancient Greek "súnopsis," which is a combination of the words for "with," or "together," and "view." It first entered the English language in the 1610s. Synonyms for synopsis include "abstract," "overview," "outline," "summary" and "condensation." The word can also be used to describe the plot of a film, play, speech or other written or spoken work.