A "grade" or level of initiation in Aleister Crowley's A.A. (aka, Astrum Argenteum, Astrum Argentium, Astron Argon - or, for those who aren't keen on Latin, simply the Order of the Silver Star). See also: Golden Dawn, Ordo Templi Orientis, etc. Crowley started A.A. after being booted out of the O.T.O for persistent poor impulse control and abysmal social skills.
The Babe of the Abyss is one of two final choices for the magician who has passed through all other levels of initiation. Such a one may either a) become a Babe of the Abyss, strip himself of all worldly concepts of self and materialism, and bond with his guardian angel, (sending etheric telegrams back via the stars), or b) become a "brother of the left hand path", i.e., black magician:
...The Grade of the Babe of the Abyss is not a Grade in the proper sense, being rather a passage between the two Orders. Its characteristics are wholly negative, as it is attained by the resolve of the Adeptus Exemptus to surrender all that he has and is for ever. It is an annihilation of all the bonds that compose the self or constitute the Cosmos, a resolution of all complexities into their elements, and these thereby cease to manifest, since things are only knowable in respect of their relation to, and reaction on, other things...
- Aleister Crowley
Scholars have interpreted Crowley's writings on the concept of becoming a Babe of the Abyss as a proto-posthumanist manifesto born out of occult-flavored existentialism. The dissolution of the self, in this case, causes the adept to literally become a bridge between the human and the numinous. The Babe of the Abyss is also interpreted in some measure by practitioners as a kind of bodhissatva figure, or "Secret Chief". Choosing the other option (left hand path) means renouncing the "guardian angel" who has facilitated progress along the other grades of initiation.
It is said that this renunciation was precisely the choice of L. Ron Hubbard, who was an "adept" of the AA prior to his founding of Scientology (a move he made after electing the left hand path, reportedly).
A more scholarly interpretation is provided by Lloyd Keane in his thesis Magick, Liber Aba and Mysterium Coniunctionis:
A Comparison of the Writings of Aleister Crowley and C.G. Jung. Lloyd writes:
The Abyss represents a barrier or "buffer" between rational and monophasic consciousness and a form of trans-rational, trans-personal consciousness which incorporates a polyphasic paradigm... Following the pattern of the World's descent myths the initiate must leave all preconceived and preconditioned notions of the subject-object dichotomy, of the tangibility of the external world, and the very existence of the initiate behind. Again, each initiate's experience would be different but the basic understanding is that "the Babe of the Abyss"...has undergone a complete shift in consciousness where all semblances of the "Pseudo-Self" have been discarded including the bond between the initiate and his or her Holy Guardian Angel.