If someone wins something "fair and square," it means that he or she has won a contest without any doubt about the outcome. The phrase, which is an English idiom, also implies that the person or team that won did so without using any unscrupulous or cheating methods. This phrase can also be used in many occasions in which someone has business dealings which are clean and on the level. "Fair and square" is a phrase that has been around for over 500 years, and it gets its meaning from the figurative meaning of "square" as honest.
It is common for people speaking the English language to use short phrases that have meanings that might not be suggested by the literal definitions of the words they contain. These short phrases are known as idioms, and they give speakers a way to add color and expressiveness to their communications with others. Idioms take their meanings from the way that they are used and understood by people in the culture. One such idiom that has to do with contests between two people or teams is the phrase "fair and square."
The party in the contest that manages to win in a manner that merits the use of this phrase often wins decisively. When the phrase is used in this manner, there is an implication that previous contests between two combatants might have been so close that their outcome was up for debate. A win in this manner, by contrast, is a total and undeniable victory. For example, someone might say, "The first two matches were way too close to call, but there is no doubt that Susan won this time fair and square."
Another way in which this phrase is used is to denote a victory that comes without any cheating or bad sportsmanship. This type of victory is also often set in contrast to a previous game that might have been marred by some sort of bad behavior. As an example, consider the sentence, "We had an umpire this time to make sure there was no cheating, so we won fair and square."
This phrase is often used in the context of business dealings that are held without any underhanded behavior by one of the business parties. There is written evidence of the phrase "fair and square" being used as early as the 16th century. It plays off the fact that something that is described as being "square" is often considered to be something that is upright and honest.