As a symbol, the Eye represents Omniscience, the all-seeing divinity. It can also represent Light, knowledge, the mind, and of a limitation of the visible.
A single eye is either symbolic of:

As the Eye of Horus, it -again


When appearing in meditations, sessions, or dreams as eyes that are watching the subject, eyes can be an indication of paranoia or possession.

The "third eye" has a symbolic meaning of its own. See: third eye.