Music written for a play. Kind of like opera but with less singing (or none) and more talking than usual. Kind of like ballet, but with less dancing (or none) and more talking than usual. While many plays included a lot of music just as a given thing, the famous, non-anonymous (!) incidental scores usually came after the plays, sometimes long after, and are (have become) as self-standing as the plays they were written to accompany. You're more likely to hear incidental music in an ordinary concert than you are to hear ballet music or opera.
Those are the nineteenth century famous ones, (the ones Wikipedia has heard about), but there are many more, including
Sibelius, Tempest, Pelleas et Melisande
Nielsen, Aladdin Prokofiev, Hamlet, Boris Godunov, Eugene Onegin
And so forth.
Most definitions you can find online include any music written for t.v. shows, movies, video games and such. But aside from a few film scores, like Antheil's Ballet Mecanique, Prokofiev's Alexander Nevsky and Ivan the Terrible, and Bokanowski's L'Ange, these other kinds of "incidental music" are probably not going to be more than ephemeral.
Incidental music is music in a play, television program, radio program, video game or some other form not primarily musical. The term is less frequently applied to film music, with such music being referred to instead as the "film score" or "soundtrack".
Incidental music is often "background" music, and adds atmosphere to the action. It may also include pieces which will provide the main interest for the audience, for example overtures, or music played during scene changes. It may also be required in plays which have musicians performing on-stage.
The use of incidental music dates back at least as far as Greek drama. A number of classical composers have written incidental music for various plays, with the more famous examples including Ludwig van Beethoven's Egmont music, Franz Schubert's Rosamunde music, Felix Mendelssohn's music for A Midsummer Night's Dream , Georges Bizet's music for L'Arlesienne, and Edvard Grieg's music for Henrik Ibsen's Peer Gynt. Parts of all of these are often performed in concerts outside the context of the play.
Modern composers of stage music include John White. One of the best known incidental music composers for British television is Howard Goodall, who wrote music for The Gathering Storm, Blackadder and Red Dwarf as well as the film, Bean.