The origins of this phrase are not very clear. Its first mention was in The Times of London in May 1960:
As far as building up a basis for profitable negotiations is concerned the two sides are back at square one. (Quotation found in Quinion, p. 238)
The phrase is believed to have its origin in the early BBC radio commentaries of soccer matches, but this seems to be only a folk story because of the long gap between the early days of radio in Britain and the first mention of the phrase in 1960. Still, the story is nice and quite convincing. On 22 January 1927, the BBC was broadcasting the first commentary on a football match. The producer of the broadcast, Lance Sieveking, wanted to help listeners to visualize the pitch and that is why he published a diagram of an eight-squared pitch to enable listeners to know what square the ball was in. The game is restarted from the goalkeeper's possession and would be called back to square one. Still, the explanation seems a bit stretched, according to Quinion (p. 238) because the game could not always be resumed from square one. The following drawing shows that the ball could be only once every four times in square one and that was when the game was restarted by the goalkeeper:
Quinion believes that a more reliable story about the origin of the phrase is the one that identifies its beginnings in a board game, where reaching a wrong square can send the player right back to the first square.
Another story claims that the phrase might have its origins in the game called hopscotch because the playground consists of a grid made up of numbered squares. The precise rules of the game vary from place to place but usually involve players hopping from square to square, missing out on the square containing their thrown stone. They go from one to (usually) eight or ten and then back to square one.
No matter how true these stories are, each of them reflects the same meaning; to go back to square one means to stop an activity and to go back to the very beginning and start again, without implying any progress, like in the following contexts:
The research was back to square one when the tests failed.
Everything was fine two days ago, but now they don’t seem to be satisfied with our work and here we are back to square one.
Nevertheless, back to square one seems to be a never-ending story.
(http://www.wethepeoplemedia.org/Articles/JacquelineThompson/IckesBackToSquareOne.html)
In Romanian, the following phrases would help convey the meaning of the English phrase: (a Lua total) de la capăt/de la început, înapoi de unde am pornit, (an începe) de la zero.