"Singularity" means failure of a man-made mathematical model, where the model (not Nature) breaks down gives meaningless numbers or blows up.
In physics history (going back over 100 years) there have been a bunch of singularities in various models (model of hydrogen atom, model of thermal radiation from a warm or hot object). They have been taken as symptoms that the math needed improvement, and they have been fixed. A singularity does not have to occur at a single point. A theory can suffer from this type of breakdown in a region of infinite volume, or on a surface of finite area etc etc. It does not mean "single point".
What the public gets told has so far been a different story. It could be that general audience likes to be told about wondrous mysteries like a "point of infinite density". Maybe science journalists have done a poor job communicating so far. Maybe people like to believe stuff that stretches their credulity. Myths have always been popular.
But among professional cosmologists (google "a tale of two big bangs" for an outreach article from Albert Einstein Institute) the cosmological singularity is used as TIME-MARKER, a shorthand for "the moment in time where our current cosmic model utterly blows up."
The cosmic singularity is also taken not as a real event but as a SYMPTOM that the classical 1915 math that cosmic model is based on fails at high density and needs fixing, or replacement.
So a number of people have been working on that and they have developed several quantized versions which do NOT blow up at the start of expansion. And so at this point the game is to TEST to see which of the alternative (non-singular) candidates gives the most accurate predictions. Observational data is scheduled to be reported in 2014 by the European Space Agency (ESA) which may help to decide which (non-singular) theory looks like a winner.
Historically, "singularity" referred to oddity, eccentricity, something irregular or out of the ordinary. That is one of its senses, in English, and that is the origin of the mathematical usage of the term.
It does not mean single point surrounded by empty space!
That mental image (suggested by the sound of the word, not the real sense of the word) is totally on the wrong track.
keepit said:
At the BB did our universe include anything other than the singularity?
The difficulty with this question is that in professional science one does not assume that the real universe ever contained a singularity.
The AEI outreach article (google "a tale of two big bangs") puts it succinctly near the bottom of the page. Most professional cosmologists would be quite surprised if it actually turned out that at the start of the current expansion the universe contained "a point of infinite density" (whatever that might mean.)
You should probably rephrase your question to be about one or more of the candidate theories that actually say something about what the universe was like at the beginning of expansion.
The model based on classical 1915 GR does not make any clear statement, it leaves the very beginning undescribed. In the most commonly used cosmic model space has infinite volume, with approximately uniform energy density growing without limit as you go back in time. So as you push the model back in time towards the start of expansion it simply becomes invalid, inapplicable, unreliable (near the start of expansion.) If you are interested in those very very early moments then you have to shift over to other models (eg. quantum cosmology) which are post-1915 based and where the energy density does NOT grow without bound. At very high energy density (approx uniform throughout space) quantum corrections can even make gravity REPEL rather than attract. So there can be a BOUNCE when very high energy densities are reached, in some of the models being studied.
People have various ideas about the OVERALL SIZE of space at the beginning of expansion, i.e. the moment of highest energy density. Space might have been infinite volume (approx unif. energy density) or it might have been some finite volume (again with nearly uniform density). Or the picture might be complicated---highly uneven--- with different patches at different density exanding at different rates and only OUR part, that the standard cosmic models cover, being uniform enough so you can talk about a moment of highest density and a definite beginning of expansion.
Personally I don't worry about the highly uneven pictures because what we can see is highly uniform (the CMB is same temperature in all directions up to one part in 100,000. Uniform to within 1/1000 of one percent. so I figure what we live in and what we have to study and try explaining is remarkably uniform and coordinated back in very early times, and can be well-approximated with uniform models. So why speculate about a totally inhomogeneous fantasy out beyond that we see no evidence of? It's interesting enough to focus on understanding what we live in without making up more complicated stuff.
And even that we have no certainty about the overall size. The portion we actually observe changes over time as more light comes in from farther away, so the "observable" size is a very poor indicator of the actual size of what has to be modeled.