An arm’s-length transaction is a transaction between a buyer and seller with roughly equal bargaining power who are trying to negotiate the best terms for their respective sides. Presumably, the seller wants the highest price possible and the buyer wants to pay the least amount possible. The majority of private party real estate transactions proceed in this way, and the selling price in an arm’s-length transaction likely represents the fair market value of the home.
An example of a deal that is not an arm’s-length transaction would be a father selling his home to his son. In that case, the father may give the son a large discount and the home would sell below market value.