Horus is the son of Osiris and nephew to Set. After Set murdered Osiris, Horus and his mother Isis set to work putting the dismembered Osiris back together and reviving him as lord of the underworld. According to one story, Horus sacrificed one of his own eyes for Osiris. In another story, Horus loses his eye in a subsequent battle with Set. As such, the symbol is connected with healing and restoration.
The symbol is also one of protection and was commonly used in protective amulets worn by both the living and the dead.
The Eye of Horus commonly, but not always. sports a blue iris. The Eye of Horus is the most common use of the eye symbol.