A square position is a situation where a trader or portfolio has no market exposure. It is commonly associated with foreign-exchange trading, but it can be applied to any type of market trade where offsetting positions can be held. A square position is also referred to as a "flat position."
Square position, like many trading terms, can take on a different nuance depending on the speaker. For an individual forex trader, a square position can refer to offsetting long and short positions in the same currency pair or to a situation where a currency trader holds no positions in the market. The reason for this confusion is that the term "squaring up" is used to describe settling open trades before the market closes. Squaring usually refers to just a few positions, but a trader could close out all of his open positions and get out of the market.