To go back to square one is to start all over again because something isn't working quite right. If you need to scrap your essay halfway through because of a flawed argument, you'd be back to square one.
Back to square one is similar in meaning to back to the drawing board. In other words, all of your supposed progress is wiped out, and you'll have to start all over again. The etymology of this phrase isn't fully known, but it's likely that it came from board games in which a mistake or unlucky break can send a player's piece back to the beginning — square one.