Who they were
Zoroaster (Zarathushtra) was the prophet whose teaching became Zoroastrianism. When he lived is genuinely unknown: traditional dating puts him in the 6th century BC, while many scholars argue from the archaic language of the hymns attributed to him for a date of c. 1500–1000 BC. He likely lived in eastern Iran or Central Asia. Almost nothing certain is known of his life; the biography of miraculous birth and the conversion of king Vishtaspa is supplied by later tradition.
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.