An Opus Number is an identity number for a piece of orchestral or choral music. It is only unique for each composer. The numbers are supposedly allocated in chronological order by composition date. In many cases, they are assigned by the composer or the publisher. In those cases, the number is prefixed by the word "Opus" or Op., with the number on scores or recordings of their works.

Many composers did not have a proper Opus Number system, and archivists, historians or musicologists devised a numbering system after their death. These numbers are properly called catalogue numbers. For example, Mozart's works are marked K or KV to indicate Ludwig von Kochel, who tried to figure out the order of Mozart's compositions. (the V is for "Verzeichnis", German for catalogue). Johann Sebastian Bach's numbers are prefixed with BWV, for the German "Bachwerkeverzeichnis" or "Bach's work catalogue".

These numbers are necessary because composers often re-visit the same material more than once. I know of at least two Beethoven settings of the Mass. These may be known by different names in different countries, but the Opus or Catalogue Number will tell them apart. There is the Mass in C Major and the Missa Solemnis; Op. 86 and Op. 123. The latter is not generally known by its key signature (D Major), but both can be identified by their Opus Number.


Source: My own observations, backed up by, and corrected by Ouroboros