A category of hymns in Byzantine Chant music, the troparion consists of one stanza of lyrics, which may be a standalone prayer or part of a series of prayer stanzas, such as Canons, which are performed in rotation throughout different times in the liturgical year, each stanza being representative of the main idea or theme of that day's sermon.
Most commonly, the term troparion is a functional synonym for the apolytikion, the daily thematic hymn dismissing the congregation at the end of Vespers.
The Theotokia, a cycle of thematic hymns dedicated to the Virgin Mary, are also troparia. Troparia with a specific figure in mind are also called odes, when referring to the lyrics in isolation from music.
The troparion form likely evolved from a simple refrain or other verse repetition used to connect thematically related hymns during a given service, and for this reason a troparion can use any of the eight standardised "tones" (modes) of Byzantine religious music, while most other hymn forms are confined to a narrower selection of tones.
Edited to add, courtesy of fellow Noder Byzantine:
One quick note on Troparion: as a suggestion, you might want to note that as a poetic form, it is not specifically musically-Byzantine, as Slavic and Arabic practice (whether Orthodox or Catholic) reflects.
Iron Noder 2022, 10/30