August is the one month where students are not present at Hogwarts. The Hogwarts staff typically leaves the castle for the month, although some do remain for all or part of the time. Filch, presumably, uses the time to catch up on cleaning. McGonagall has no other home than Hogwarts (Pm). Snape, however, spends his weeks off in his home in Spinners End, Cokeworth (HBP2). Also during the summer, new staff is hired, book lists are mailed to students, welcome letters are sent, OWL and NEWT test results are sent to those who took those tests the previous year.
The following people have birthdays in August:
August 11 = Ginny Weasley
August 18 = Celestina Warbeck (Pm)
August 19 = Tina Goldstein (WFT)
August 22 = Percy Weasley
August 26 = Dolores Umbridge (Pm)