An arm’s length transaction is an agreement between a willing buyer and a willing seller who are unrelated.
If a man sold his son a car, this would not be an arm’s length transaction. The man would probably be inclined to give his son a bargain price. If a company sold raw material to a subsidiary, this would probably not be an arm’s length transaction because the parent company would be inclined to give the subsidiary a good price. Let’s say a judge was deciding an important case for a bank. If the bank gave the judge a 1% loan this would probably not be an arm’s length transaction because the bank would be hoping to influence the judge. If you put an ad in the paper to sell your car and end up selling it to a complete stranger, this probably would be an arm’s length transaction.