פיוט – pl. piyutim – Hebrew, and occasionally Aramaic, liturgical poetry, meaning poems added to the prayer service. Piyutim appear especially in the machzor (holiday prayerbook), but also in the daily siddur, especially in the earlier period of their composition.
The earliest piyyutim were written in Eretz Yisrael during the Byzantine period when the form of the prayers was not yet fixed, and could replace parts of the service; among the most well known payatanim (composers of piyut) from this early period are Yose b. Yose, Yannai, and Eleazar b. Kallir (or ha-Kalliri). This practice was discontinued with the standardization of the prayer texts, although piyyut continued to flourish during the early Muslim period and into the period of the Rishonim. There are many different technical forms that piyutim take, and they tend to be inserted in particular places in the service.
In medieval Ashkenaz, there developed a tradition of writing commentaries on piyyut as well as composing original piyyutim.
In contemporary practice, the inclusion of particular piyutim as well as the practices around their recitation often distinguish the different nuschaot (rites or versions) of the machzorim of diverse communities. Many piyyutim, both historically and today, are sung. You can access the words and many different melodies on the National Library of Israel‘s Piyut site.