A "BWV number" is a number that uniquely identifies one of Bach's compositions. These numbers originate with the Bach-Werke-Verzeichnis (Bach Works Catalogue) compiled by Wolfgang Schmieder in 1950. An up-to-date list of BWV numbers can be found on Wikipedia's ➟ List of compositions by Johann Sebastian Bach.
Unlike catalogues of compositions by some other composers, BWV numbers aren't in any sort of chronological order. Most of Bach's pieces were not published in his lifetime, and in some cases, we don't know when he wrote them either. Instead, they're grouped thematically. Pieces with BWV numbers near each other tend to have similar instrumentation and musical styles.
It's often very useful to refer to Bach pieces by their BWV numbers, to be clear about which piece we're referring to. Bach didn't particularly care about titles, the titles his pieces do have are often translated inconsistently into English from German, Italian, or Latin, and many of the titles are duplicates of each other.
Hofstadter refers to Bach's pieces by their informal English titles. On this wiki, we also include the BWV numbers, so you can look for the pieces more easily.
BWV numbers don't entirely do the job of referring to pieces within the Musical Offering (Musikalisches Opfer), many of which appear in GEB. BWV 1079 covers all of the pieces in the Musical Offering, and there's no consistent order in which these pieces are performed or published, so we have to call them by their inconsistent names anyway.