For much of the world, supernumerary means exactly what you think it means based on the word's parts: super (over or exceeding, e.g., superimpose, supernatural ) + numerary (as in number) = a number that is higher than an expected number. It can be synonymous with superfluous, excessive, overabundant.
In the world of theatre, though, it means something else.
The term comes from the Latin supernumerarius, which was what they called someone who was hired to appear on stage in crowd scenes or, for opera, in small, non-singing roles.
Supernumeraries are the theatrical equivalent of movie extras, which makes sense considering that supernumerary and extra are synonymous. Unlike movie extras, though, theatrical supernumeraries need to have some acting chops. They are cast not only as random background people milling about, but as flag-bearers, royal assistants, live statues, fishermen, and on and on. Even though they have no lines, they still might have stuff to do, and they need to be in character.
Some people make a living as supernumeraries, and larger opera houses might even have their own troupe of supernumeraries. But many do it just for fun and to get involved in the theatre. Sometimes, people well-known in other areas get the craving for theatre and take on supernumerary roles. Supreme Court Justices Anthony Kennedy and Ruth Bader Ginsberg, for example, have performed with the Washington National Opera; their last performance (as far as I can gather) was in Strauss's operetta Die Fledermaus.
It's a nice, important-sounding word, too, front-loaded with that super-. Being "an extra in a play" just doesn't have that hifalutin ring that being "a supernumerary in the theatre" does.