The third eye is a term vague enough to be shoehorned into just about any New Age claptrap.
In Hinduism, it is the chakra on the forehead between the eyebrows. "Opening your third eye" is usually meant as "achieving enlightenment."
Some psychics and other woo-meisters claim opening your third eye will give you some kind of psychic powers like ESP. Woo revolving around the pineal gland often invokes the third eye.
Some say you can "feel" your third eye if you press your finger between your eyebrows and move it around until you get a "funny" feeling. In reality, you'll just make yourself look like a jackass.