It's called a Pull Quote. It's used in newspapers and magazines to draw you into an article as you leaf through the pages, I guess it serves basically the same purpose in blogs.
It works best in magazines or newspaper layouts where the pull-quote exists outside of the normal eye-path when reading the article. Then you avoid the "Hey, I just read that" moment, but still pull people in who are leafing through.
But, web pages are not typically laid out in such a way to allow for that.
http://en.wikipedia.org/wiki/Pull_quote