The Hawkeye is a mask currently exclusive to Twilight Princess. It is a purchasable item from Malo Mart after completing a little mini-game of archery training with Malo and Talo and will cost 100 Rupees. This mask - as the name suggests - looks like the face of a bird. When worn, it allows Link to see things much closer like wearing a pair of binoculars.
The most interesting use of the mask, however, is in tandem with the Hero's Bow. When used together the mask functions like a scope for the weapon, allowing Link to use his bow to snipe enemies from afar with ease and precision. It should be noted though that this cannot be used with Bomb Arrows.