The bibliographical definition of an edition includes all copies of a book printed “from substantially the same setting of type,” including all minor typographical variants.
The numbering of book editions is a special case of the wider field of revision control. The traditional conventions for numbering book editions evolved spontaneously for several centuries before any greater applied science of revision control became important to humanity, which did not occur until the era of widespread computing had arrived (when software and electronic publishing came into existence). The old and new aspects of book edition numbering (from before and since the advent of computing) are discussed below.
According to the definition of edition above, a book printed today, by the same publisher, and from the same type as when it was first published, is still the first edition of that book to a bibliographer. However, book collectors generally use the term first edition to mean specifically the first print run of the first edition (aka "first edition, first impression"). Since World War II, books often include a number line (printer's key) that indicates the print run.
A "first edition" per se is not a valuable collectible book. A popular work may be published and reprinted over time by many publishers, and in a variety of formats. There will be a first edition of each, which the publisher may cite on the copyright page, such as: "First mass market paperback edition". The first edition of a facsimile reprint is the reprint publisher's first edition, but not the first edition of the work itself.
The Independent Online Booksellers Association has a A First Edition Primer which discusses several aspects of identifying first editions including publishing and specific publishers way of designating first editions.
The classic explanation of edition was given by Fredson Bowers in Principles of Bibliographical Description (1949). Bowers wrote that an edition is “the whole number of copies printed at any time or times from substantially the same setting of type-pages,” including “all issues and variant states existing within its basic type-setting, as well as all impressions.”