Shiva is sometimes called Trilochana, the three-eyed one, because in the center of his forehead is the eye of wisdom, or jnana chaksu. This half-lidded third eye also represents his destructive energy that if let loose would destroy the whole world. Half-closed eyes mean that his mind is absorbed in the inner Self while his body is engaged in the world. Shiva is the Master of Yoga, as He uses His yogic power to project the universe from Himself. The half-open eyes symbolize His yogic posture, engrossed in meditation.
However viewing the outer world with inner wisdom. Closed eyes would represent one wholly introverted. Fully open eyes would signify total extroverted ness. The symbolism of Shiva's half-closed eyes, however, indicate that He is fully conscious of the within and the without. He understands the world outside to be only a reflection of the Self within. With this intuitive experience, His actions sing the song of the Self in all transactions in the world.
It is when the Lord opens His eyes, a new cycle of creation emerges and when He closes them, the universe dissolves for creation of the next cycle. The half-open eyes convey the idea that creation is going through cyclic process, with no beginning and no end!
Hari Om Tat Sat ~ Jai Trayambaka Deva!