The month of August (Latin: Augustus) is named after Augustus, the founder of the Roman Empire and its first Emperor, ruling from 27 BC until his death in 14 AD. Until Augustus' time the month of August was called Sextilis (named so because it had been the sixth month of the original Roman calendar, and the Latin word for six is sex).

Commonly repeated folk lore has it that August has 31 days because Augustus wanted his month to match the length of Julius Caesar's July, but this is an invention of the 13th century scholar Johannes de Sacrobosco. Sextilis in fact had 31 days before it was renamed, and it was not chosen for its length. According to a senatus consultum quoted by Macrobius, Sextilis was renamed to honor Augustus because several of the most significant events in his rise to power, culminating in the fall of Alexandria, fell in that month.

More Info: en.wikipedia.org