The Message Box is a box which holds messages. Everytime the player plays Zoo Tycoon, for example, when it says "Name of Animal is not happy", meaning that the animal is not happy. These are examples of messages:
Orca 1 is not happy.
Orca 1 can't find any food.
Snow Leopard 1 has escaped into Exhibit 1.
Your zoo is running on low money.