Fixing the eyes on an object is a specialized technique in Hatha Yoga and it is known as Drishti (gaze). Drishti means fixing the eyes, not allowing the pupils to move to the left or right, up or down. This can be done with the eyes open, half open or closed. The gaze is thus usually fixed on two points, namely, the tip of the nose and the mid-point between the eyebrows.
Lotus pose employs the tip of the nose gaze. Adept pose or Siddhasana adapts the mid-point between the eyebrows.
Keeping the eyes fixed and steady helps to arrest the wandering mind, just as holding the apparatus of speech (the lips, cheeks, inside the mouth and tongue) motionless helps a great deal to stop the process of speaking to oneself. It exerts less stress on the ciliary muscles of the eyes.
The gaze may be fixed with the advantage on external objects like a picture, an image, a symbol like om or on the flame of a small lamp used in worship. This is done in trataka.
Drishti is also applied effortlessly and naturally in more advanced yogic practices of meditation, such as Shambhavi mudra and Khechari mudra. In these mudras, the eyes are not fixed consciously, but with the deeply absorbed and silent state of the mind, the pupils become motionless automatically.