The month of August was originally named Sextillis because it was originally the sixth month instead of the 8th on the Roman calendar. It was named for Augustus Caesar who is considered the first Emperor of Rome.
The word comes from the Latin word “Augure” which means “to increase” . The name Augustus was given to all Emperors because it meant “esteem”. Augustus was the nephew of Julius Caesar, who named a month after himself… July.