Square one is the point where you start from, so back to square one is starting again from the very beginning. Example: "After all that work, they decided not to hire me." Reply: "Back to square one."

There may have been a failure or a loss or some other reason to start again, when you have to go back to the beginning and "start from square one." Example: "What will you do if you lose everything you have." Reply: "Go back to square one, and start again."