Who is Sauron?
Sauron (or Þauron (Thauron); "The Abhorred"), the eponymous Lord of the Rings, was a fallen Maia, creator of the One Ring, and the most trusted lieutenant of Melkor (Morgoth, the first Dark Lord). After Melkor's defeat by the Valar, Sauron in time became the second Dark Lord and strove to conquer Arda by creating the Rings of Power.
In the Second Age, he was defeated in the War of the Last Alliance by Elves and Men united under kings Gil-galad and Elendil. In the final battle, Isildur managed to cut off the One Ring from Sauron's finger, dismantling Sauron's corporeal form and power. After lying dormant and regaining strength for centuries, Sauron returned to power late in the Third Age and would be permanently defeated in the War of the Ring by the destruction of the One Ring by Frodo Baggins.
He was called Gorthaur, the Cruel by the Sindar.
What is the eye of Sauron?
The Eye of Sauron, or Great Eye, was a symbol adopted by the Dark Lord in the Third Age. It was said that few could endure its terrible gaze. The Eye was used as a symbol on armor and banners of Mordor, representing Sauron's quasi-omnipotence.
The Eye of Sauron, also called by various names, was the symbol of Sauron the Dark Lord following the loss of the One Ring. This symbol was adopted to show his unceasing vigilance and piercing perception and was displayed on the weaponry of his servants, or at least the orcs.
With it, Sauron searched for and tracked the paths of the Ring-bearer Frodo Baggins at the end of the Third Age.
It is unknown when the Eye of Sauron was formed. At the apex of Barad-dûr, the Eye was a flaming, visible, though perhaps not tangible presence during the events of The Lord of the Rings, made clear when it appeared through a window when clouds parted in Mordor.
In Peter Jackson's The Lord of the Rings film trilogy, the Great Eye is a gigantic eyeball composed of energy that sits atop Barad-dûr.
In Monolith's sequel to Shadow of Mordor, Middle-earth: Shadow of War the Eye depicted in Jackson's trilogy is the actual manifestation of Sauron and the wraith of Celebrimbor, the Elf who forged the rings of power, in a state of perpetual combat. When the ring is destroyed and Barad-dûr falls, the Eye implodes and Celebrimbor is presumed free.
Where is the Eye of Sauron located?
Located in northwest Mordor, near Mount Doom, the Eye of Sauron keeps watching over Middle-earth from its highest tower. The Lieutenant of Barad-dûr is the Mouth of Sauron, who acts as an ambassador and herald for Mordor and Sauron.
What does it look like?
Throughout The Lord of the Rings, "the Eye" (the Red Eye, the Evil Eye, the Lidless Eye, the Great Eye) is the image most often associated with Sauron. Sauron's Orcs bore the symbol of the Eye on their helmets and shields and referred to him as the "Eye" because he did not allow his name to be written or spoken, according to Aragorn (a notable exception to this rule was his emissary, the Mouth of Sauron). Also, the Lord of the Nazgûl threatened Éowyn with torture before the "Lidless Eye" at the Battle of the Pelennor Fields.
Frodo had a vision of the Eye in the Mirror of Galadriel:
The Eye was rimmed with fire, but was itself glazed, yellow as a cat's, watchful and intent, and the black slit of its pupil opened on a pit, a window into nothing.
Later, Tolkien writes as if Frodo and Sam really glimpse the Eye directly. The mists surrounding Barad-dûr are briefly withdrawn, and:
one moment only it stared out ... as from some great window immeasurably high there stabbed northward a flame of red, the flicker of a piercing Eye ... The Eye was not turned on them, it was gazing north ... but Frodo at that dreadful glimpse fell as one stricken mortally.
Inspired by these, the eye of Sauron accessories was born.