From my current understanding, it was the title given to the ruler of the Persian Empire. I've read other things that it was in Greek mythology or something along those lines. I was hoping someone could clear it up for me.
Achaemenes was the ancestor of Darius I, or at least was the eponymous clan founder. Whether or not there was ever a living person whose name was "Achaemenes" cannot be proven, but the lineages of Darius and Cyrus claimed rights to rule Persia by descent from the tribal ancestor, from whom the dynasty (and the tribe) derive their identities. The Achaemenids are those descended from Achaemenes.
Waters, M. (2004). Cyrus and the Achaemenids. Iran, 91-102. Chicago