To Explain the uniqueness of a mammal I will talk about how a mouse and a whale are similar and are both mammals. To say that they give birth the live young is not enough because snakes and some frogs do also. To say that the are warm blooded is also not enough because birds are also warm blooded. To say that they are breathing and have a backbone is not specific enough because lizards and toads both have these characteristics.
Hair is used to insulate and keep the body warm in a large variety of climates.
The Mammary glands are what produce milk for the young when they are not able to consume solid foods. Whales and other sea dwellers produce the richest milk. It contains the most fat so that the young will gain the most wieght the fastest and will also help in developing the layer of blubber that insulates the body from the extreme coldness of the sea.