Definition: Founded by Cyrus II (the Great) in the area of Babylonia (in southwest Iran and Mesopotamia), the Persian Achaemenid dynasty ran from about 560-330 B.C., when Alexander the Great defeated Darius III of Persia. The Achaemenid Empire was divided into twenty satrapies which allowed relative regional autonomy to the areas. At its height under Darius, the Achaemenid empire stretched from the Indus River to Egypt.
Although the official language of the Achaemenid Empire was Old Persian, the most common language was Aramaic. Most of the ancient references to the Achaemenids come from Greek sources (Herodotus, Aeschylus, Xenophon, and Ctesias).
Reference: "Seals and the Elite at Persepolis: Some Observations on Early Achaemenid Persian Art," by M. B. Garrison; Ars Orientalis, (1991), pp. 1-29.
Examples:
When talking about the Persian Wars, it is the Persian Empire of the Achaemenids that the Greeks fought.

