Designed to resemble the eye of a falcon, this symbol is called the Eye of Ra or Eye of Horus represents the right eye of the Egyptian Falcon God Horus. As the udjat (or utchat), it represented the sun, and was associated with the Sun God Ra (Re).
The mirror image, or left eye, represented the moon, and the God Tehuti (Thoth). (A very similar concept of the sun and moon as eyes appears in many religious traditions)
According to legend, the left eye was torn from Horus by his murderous brother Seth, and magically restored by Thoth, the God of magick. After the restoration, some stories state, Horus made a gift of the eye to Osiris, which allowed this solar deity to rule the underworld. The story of this injury is probably an allusion to the phases of the moon as the eye which is "torn out" every month.
Together, the eyes represent the whole of the universe, a concept similar to that of the Taoist Yin-yang symbol. Spiritually, the right eye reflects solar, masculine energy, as well as reason and mathematics. The left eye reflects fluid, feminine, lunar energy, and rules intuition and magick. Together, they represent the combined, transcendent power of Horus.
The Eye of Horus was believed to have healing and protective power, and it was used as a protective amulet, and as a medical measuring device, using the mathematical proportions of the eye to determine the proportions of ingredients in medical preparations) to prepare medications.
The Masonic all seeing eye, the Eye of Providence symbol found on American money, and our modern Rx pharmaceutical symbol are all descended from the Eye of Horus.