1. "Son of Aaron": It is a patronymic surname, meaning "son of Aaron". Aaron was a biblical figure, the brother of Moses.
2. "From the homestead of Aaron": It could also be a topographic surname, meaning "someone who lived at the homestead of Aaron".
The surname Arrington is most common in the United States, particularly in the South. It is also found in England and Ireland.
It is important to note that these are just possible meanings and the exact origin and meaning of the name may vary depending on the individual family's history.