That's the number of times that post has gotten a +1 on Google+. You may notice that none of the posts before or after it have any Google+ stats, and that's because Google+ wasn't around then...or, if it was, I didn't use it. In case you're wondering, that blog post is a particularly mundane piece of writing about watching American Idol and feeling old.
As I looked through the rest of my stats, the same phenomenon occurred two other times, on seemingly random posts, neither of which got many comments.
The most confusing part of this whole +1 phenomenon is that the number in the column to the left of the date is the number of page views. So, while I may have 65,475 +1s on my blog post about three little boys talking about the Titanic tragedy, it appears that only 69 people actually went to the page to read the thing that they +1d.
I am baffled.