No, I think it's the # of Alexa users, per million, that visit the site on a given day. For example, when FR peaked near 1,000, that's 1,000 visits per million users per day; in other words about one out of every 1,000 internet users visited FR on that day.
I thought the number stood for daily "hits" or visits, until I tried an Alexa search on my main website, The Xenophile Historian. According to my counter I'm getting about 800 hits a day, but the number Alexa gave me is almost 4,000. Hmmmm . . .
http://www.alexa.com/data/details/?url=xenohistorian.faithweb.com