An arms-length transaction occurs between a buyer and a seller on the open market. Both parties act according to their own self-interest with the buyer wanting the lowest possible price and the seller wanting the maximum price. Fair market value of a home is determined by the closing of an arms-length transaction.
Many transactions are not arms-length, such as a parent selling a home to their child. Short sales are usually required to be arms-length transactions so that the bank taking the loss is not being taken advantage of by a buyer and seller who are colluding on an artificially low sale price.