What does "last August" refer to?

Generally, the last August before the current month. If you said this in December you'd be referring to the August of the same year, but if you said it in January you'd be referring to last year. If you said it in August, though, it would mean one year ago.

There's slight ambiguity shortly after the month, when reasonable people might mean either the past month or thirteen months ago. Usually context makes this clear.

Last August will generally refer to the August of the previous calendar year.

If it is September 2010 and I mention what we did "last August", I almost certainly don't mean August 2010 (last month), but rather August 2009.

August of the same calendar year would generally be discussed by saying "in August". This applies whether it is June or October.

For example:

"Is Margaret coming in August?" (August is later in the year)

"That library book was due in August." (August has passed)

If your librarian tells you your book was due last August, you're going to be paying a much higher fine.