"Incidental music" is a term describing music to accompany stage plays. In the nineteenth century especially, theatres often used orchestral music as introductions, interludes, entr'actes, and to accompany bows. It might also cover scene changes, or heighten the effect of stage action as movie music does today. (I think the last use accounts for the term "incidental music," since in such a case the music is associated with specific "incidents" within the plot.)
At any rate, some incidental music has gained a life of its own--perhaps the most famous example is Mendelssohn's march written to accompany the wedding procession in a production of Shakespeare's "Midsummer Night's Dream." Mendelssohn made an orchestral suite from his music for the play which became highly successful as a concert work, and the wedding march has been used at probably hundreds of thousands of weddings since--in such a 'traditional' use, it's generally paired with the Wagner Wedding March associated with the parody words "Here Comes The Bride." The Wagner would be the processional piece, accompanying the bride as she walks up the aisle, and the Mendelssohn would be the recessional, accompanying the newlyweds back down it again.
My sense is that expressly written incidental music has become quite rare indeed today--most incidental music you hear in modern productions is recorded music, usually presented incompletely by the use of a convenient 'fade out,' like a swatch of fabric cut to length.