History of the star: A white star situated in the mouth of the River Eridanus. Achernar is from Arabic Al Ahir Al Nahr (1), "End of the River".

This star is supposed to be one of the Tre Facelle in Dante's Purgatorio notwithstanding its invisibility from Italy (the three stars of the Tre Facelle being Fomalhaut, Achernar and Canopus).

[Star Names, Their Lore and Meaning, Richard Hinchley Allen, 1889].  

Robson (*) says this star is symbolized as the "Cherub and Sword".

The astrological influences of the constellation: According to Ptolemy all the stars with the exception of Achernar are like Saturn. Eridanus gives a love of knowledge and science, much travel and many changes, a position of authority, but danger of accidents, especially at sea and of drowning. (Robson*).  

The general astrological influences of the star: It gives success in public office, beneficence, and religion. (Robson*).

High offices in the church. Success by giving good morals, faithful adherence to one's religious beliefs or philosophical inclinations. Happiness and success. (Fixed Stars and Their Interpretation, Elsbeth Ebertin, 1923). 

References:

*(Fixed Stars and Constellations in Astrology , Vivian E. Robson, 1923)