In applying this piece of advice to our form practice we have to be selective in choosing which attributes of these two animals we wish to emulate. In the case of the tiger we are concerned with the relaxed, padding movements which contain the potential for swift and terrible action should it be required. If you study the way a tiger moves you will notice how once its leg touches the ground the whole of the bodyweight follows, yet without jarring and in a relaxedly-controlled manner.
When practising the form we should move like a tiger in slow-motion, full of powerful grace and in command of our environment. Our every movement should also contain the kind of relaxed awareness that may instantly be translated into active response should danger threaten.
Gazing like a hawk involves making full use of the eyes, including the peripheral vision so that as we do form we are aware of all that goes on around us, but are not fixated on any one object. Like the controlled awareness in movement of the tiger, the gaze of the hawk is not startled because it is aware of all that is going on around.
Generally speaking, in the form the eyes follow the movement of the front hand but they do not stare fixedly for this would preclude the use of peripheral vision. This type of vision is most obviously used in Step Back Repulse Monkey where the head follows the body but the eyes must be able to see out of their corners the fingers of both hands.
(From: The Tai Chi Classics as translated by Nigel Sutton)