Eye motif is used a lot on handmade rugs specially and Turkish area rugs and Caucasian Rugs.
See the Eye motifs on center of the rug
It is believed that eye motif protects the household from "evil eye" the harmful looks of others with jealous intentions. That is a motif used in Turkish culture for thousands of years as we know from the archeological researches and even now days many people in Turkey has instinctive beliefs that the eye motif is protective against the evil eye and it brings good luck to household, that is an important sign in the culture.
Sometimes the eye motif is used in different meaning than protection on rugs, it may also represent the "third eye" which sees the unseen behind the material universe, it represents the higher being. Eye motif is mostly woven on rugs in geometrical shapes and sometimes it is woven with blue color which is the actual color of evil eye protection.