A point at which the curvature of spacetime becomes infinite. Singularities can form — for example — when too much matter is squeezed into a region which is too small. Singularities are found at the center of a Black Hole, at the beginning of the Universe in the Big Bang, and at the end of the Universe (if it ever comes) in the Big Crunch. Many scientists believe — though there is no solid evidence — that all singularities in the present Universe lie hidden behind Event Horizons. This is the "Cosmic Censorship Conjecture".
Come, you lost Atoms, to your Centre draw,
And be the Eternal Mirror that you saw:
Rays that have wander'd into Darkness wide,
Return and back into your Sun subside.
From Farid al-Din Attar's
The Conference of the Birds