The Eileen Head is simply Eileen Galvin's head, but her skin is scarred and diseased-looking and her eyes are bloodshot. Her eyes twitch erratically and follow Henry around the room, ignoring Eileen.
Eileen makes no comment on it, giving the possibility that the head is invisible to her (in the same level, it is revealed Eileen can't see the Halo of the Sun). The head moans and breathes quite heavily. Her eyes will light up and flicker if zapped by the stun gun.
Since the Otherworld in Silent Hill 4 is most likely caused by Walter Sullivan, it may be a reflection of his thoughts or psyche. Eileen was supposed to be another sacrifice, but she survived, which the scars may represent.
Her heavy breathing sounds as if she is using a breathing tube, like the ones used in hospitals. Her breathing may also be interpreted as being sexual and orgasmic, as if she is having sex or is masturbating. This could allude to conception and her role as a sacrifice, since she is the "Mother Reborn".
The head may represent Henry's violation of Eileen's privacy. Throughout the game, Henry may repeatedly check Eileen through the peephole. Although it can be argued Henry is doing it to see if Eileen is okay, he is still spying on her. The head may be an inversion of this - now, Henry is the one being watched. However, the head still appears no matter what, regardless of how often Henry checks on Eileen. It is unknown if this is because this theory is incorrect, or simply developer oversight.
Another theory is that the head represents Henry's concerns for Eileen's safety. It is evident that Henry cares about Eileen. He doesn't want Eileen to die or be sick, and he isn't certain whether or not she's still alive during the hospital level. Henry coming (literally) face-to-face with a diseased-looking Eileen is likely uncomfortable for Henry and a manifestation of his fears.
Another theory is that the head is Eileen's monster and manifested by Eileen's feelings, and a subconscious manifestation of her internalized trauma from being beaten and nearly killed.