The Eye of Horus is an ancient Egyptian symbol. However, turn of the century occultism and then new age beliefs adopted the symbol, often placing with within an equilateral triangle. While the eye is ancient, this depiction within a triangle is not.
Those who use the symbol often see it as representing knowledge, enlightenment and insight, particularly into spiritual and esoteric matters, although there are certainly other interpretations as well.
Perhaps the most famous depiction of the symbol is in an image of Aleister Crowley where it is emblazoned on his hat.
The eye might face left or right.
Some connect it with the Eye of Providence, which exists within Christian and deist contexts. This is the watchful eye of of a superior power surveying humanity. This connection is particularly emphasized by conspiracy theorists who believe in an overbearing New World Order which inserts its own pagan or Satanic images into otherwise innocuous contexts.