We're not fans of this method, because it creates a sloppy scorecard. But especially for beginners and mid- and high-handicap golfers, it's pretty pointless. After all, if you're in these categories, you won't be making many (or probably any) birdies; you might not even be making many pars. Your scorecard will be full of nothing but numbers with squares around them.
But because it's a PGA Tour thing, some golfers like to do it this way. So one circle represents a birdie, and a score circled twice represents an eagle or better. One square represents a bogey, while a score with two squares drawn around it represents a double-bogey or worse.