Who they were
He probably lived in eastern Iran or Central Asia, among herding peoples who had not yet reached the Iranian plateau: the world of the hymns has cattle, chariots and rival priests in it, and no cities, no Persia and no writing. Almost nothing certain is known of his life. The biography of the miraculous birth, the persecution and the conversion of king Vishtaspa comes from tradition many centuries later, and the seventeen hymns called the Gathas are the only text anyone argues is his own.
What they did
The Gathas — seventeen hymns in Old Avestan attributed to him — form the core of the Avesta, Zoroastrian scripture. His teaching centered on one supreme creator god, Ahura Mazda, on the cosmic struggle between truth (asha) and the lie (druj), and on individual moral choice. These ideas are often cited as influential on later religious thought, though the extent of that influence is debated.
Legacy
Zoroastrianism became the dominant religion of pre-Islamic Iran across three empires. The Greeks knew Zoroaster as a legendary sage, and his name returned to European culture much later, notably in the form Zarathustra.