An arms length transaction involves two independent parties and each is attempting to get the best deal possible.
For example, if your mother is selling her two-year old car to you for $7,000 and the blue book wholesale value is $14,000, that is NOT an arms length transaction. Your mother is giving you a very good deal instead of attempting to get the fair market value of the car.
In an arms length transaction, the seller of a car attempts to get as much as possible for the car from an independent person who is striving to get the car for the lowest possible price. Both parties probably know the retail value and the wholesale value of the car and both want the best price: the seller is attempting to sell the car at a price that is close to the retail value and the buyer is attempting to buy the car for the wholesale value or less.