The Eye was bestowed to Azimuth by the Dimension Pillar, and "served as [her] link to the Pillar", augmenting her natural powers.[Blood Omen/3] It amplified her talents as an "explorer of alien realms", and operated as a lens which transcended the Material Realm, enabling her to perceive other "realms" or "planes" in Nosgoth – probably including the Spectral and Demon Realms.[1][Blood Omen/8][Blood Omen/Miscellaneous] When the Balance Guardian, Kain, recovered it, the Eye was red, with a vertically-oriented slit pupil, and splayed against what appeared to be a metallic mount.[Blood Omen]
The Eye was not literally Azimuth's "real" third eye, in the sense that it manifested as part of her on her face or body. This can be construed from an official render of her hosted at Dark Chronicle, which depicts her with only two eyes and no evidence of a third.[3] Presumably, the Eye was instead an accessory, much like the majority of the other Pillar tokens Kain discovered.[Blood Omen]
Material from Legacy of Kain: Defiance establishes Azimuth's long-time links to, and worship of, the Hylden. Given that the Hylden were captive within the Demon Realm during her entire lifetime and tenure, the Eye may have had a significant facilitating role in her encounters and communication with her masters.[4][5]