The term "Singularity", as used in this article's context, is an analogy to the well-known singularity in physics, the black hole, where you cannot see beyond the event horizon because light cannot escape from it. In a similar manner, we cannot see (or imagine) what's beyond the Consciousness Singularity because it is beyond our cognitive and imaginative capabilities.
The Consciousness Singularity bears no relation to the Technological Singularity, made famous by Vernor Vinge, and which involves the creation of smarter-than-human machines. Nor is it synonymous with Tielhard de Chardin's Omega Point.
To get a better intuition for the Consciousness Singularity, imagine, if you will, what a monkey or a rat would experience if suddenly its consciousness became like that of a human. Before the transition, it would be incapable of imagining what it's like to have human consciousness simply because it's beyond its limited cognitive capabilities. In the same manner, our species will undergo such abrupt transitions in consciousness of such magnitude that we cannot even begin to fathom what these new states of consciousness are like.
At the Consciousness Singularity, history as we know it, will cease. The universe, as we experience it now, will cease. Consider the most transcendent and mystical states of consciousness that have yet been experienced by mankind: these will pale in comparison with what's to come.
At the Consciousness Singularity, our consciousness will be expanded beyond the confines of an egocentric sense of self to include transpersonal experiences and transcendent self-identity. This new existence will be both a form of collective consciousness and a form of expanded individual consciousness. Though sounding like a contradiction, these two descriptions of transcendent consciousness are really flip sides of the same coin. The Consciousness Singularity is so far beyond our normal consciousness, that we cannot even begin to comprehend it, much less imagine what it's like to experience directly, unless we ourselves experience or have experienced transcendent states of consciousness.
S. Mikula, 2001
This is the first known articulation of the Consciousness Singularity.