How would you describe a black hole to a complete layman? Non-astrophysicist visitors to Black Hole, will most likely barely make it past the introduction before getting lost in the technical details. Moreover, the Wikipedia article does not teach laypeople how to think of a black hole, or give them a better intuitive sense than pop culture references to black holes, some of which are really awful!* So, please explain the concept of a black hole in a way that won't glaze over the eyes of your typical English or Business major.
*For examples, and the pop-culture smearing of the concept of black hole together with other gravitational anomalies, see:


*

*Black Holes in Fiction.

*Portable Hole.

*Wormholes  in Fiction.

*White Holes in Fiction.
 A: The answer really depends on how much detail you want.  But for a basic answer this is what I tell people:

A black hole is simply a region of
  space from which no light or
  information can escape.  The reason
  for this is that the density of matter
  in that region has become so high that
  the escape velocity, the speed needed
  to get out, is larger than the speed
  of light and since nothing can travel
  faster than the speed of light, nothing
  can escape.
The point where the escape velocity is
  equal to the speed of light around a
  black hole is known as the event
  horizion.  The distance from the
  center of the black hole to the event
  horizion determines its size.  Black
  holes are small.  A solar mass black
  hole is only about 3 km in radius and
  that diameter scales linearly with
  mass.
Black holes are not cosmic vacuum
  cleaners that "suck" everything nearby
  into it.  It behaves just like any
  other massive object.  If you were to
  suddenly replace the Sun with a black
  hole of the same mass, the only thing
  that would happen on Earth is that it
  would get really dark and cold.  It
  would not effect the orbit at all.  If
  you got in really, really close, there are
  some weird effects but you would most
  likely be ripped apart by tidal forces
  long before you got there to measure them.

At that point I answer any additional questions that might come up.
A: Both above answers are well worded, succinct, and not terribly confusing. But sometimes you have go one step further into simplicity.

Imagine the fattest person you possibly can, like Bender when he became Human. Surround this person with a gigantic buffet. What happens next is kinda like a black hole, except change the buffet for all matter and energy, and the fat person with a teeny weeny rip in the very fabric of space and time.

Now, this explanation bypasses quite a bit about black holes, but for some people this may be the best answer for them. Hopefully they will ask questions after, so you can more fully explain black holes.
I find that when answering scientific questions (I should point out right about now that I am merely an enthusiastic layman), it's best to understand the person who is asking the question, and answering any followup questions. You have to find the best description for that person/audience. In short, there will never be a 'one size fits all' answer for any scientific question. You have to see from the perspective of the person asking the question in order to best answer that question.
A: Personally I'm not entirely sure how much technical detail you require, only in a generally digestible fashion. However, given that I have recently read answers provided to numerous questions regarding black holes*, formulated for the 'general reader' but by someone who, to drastically understate, certainly knows much, much more than myself, I'll quote:

A black hole is an incredibly dense
  celestial object containing so much
  mass it has generated a powerful
  gravitational field from which not
  even light can escape. Anything that
  falls into a black hole will be
  crushed out of existence.
Black holes are spherical and expected
  to be spinning, dragging the spacetime
  continuum like honey around a spinning
  spoon. In these confused regions of
  spacetime, it won't be clear whether
  you're travelling through time or
  space or both.
Just like any object that hits the
  black hole, light too will be
  swallowed completely and quite
  possibly forever. Light that misses
  the black hole, but passes very close
  to it will be deflected onto a new
  course through space.
Nothing, not even information is
  expected to be able to escape from a
  black hole. This s contentious because
  if, as Stephen Hawking suggests, black
  holes eventually evaporate and die,
  they must be radiating particles. In
  turn, it should be possible to detect
  and measure these particles, but
  currently none of our telescopes are
  able to get any readings when pointed
  at a black hole - these areas are void
  of any information. So, to resolve
  this contradiction , it's suggested
  even information is sucked into the
  heart of the black hole.
We don't know what happens at the
  centre of a black hole. Our current
  theories break down because they can't
  deal with infinitely dense objects.
  So, physicists are trying to develop
  new theories of gravity to answer what
  lies at the bottom and whether they
  lead anywhere. Called a singularity, 
  one is thought to exist at the centre 
  of every black hole.

This may be far less technical than you desire - let us know if so. Though, even so it is an easy read with enough of an idea and general knowledge to be contributed, I believe.
*Source: BBC Focus, Brian Cox, April 2011
A: Here's my shot without appealing to concepts that are unique to math or physics.

Newton discovered that the strength of gravity of an object gets bigger as the object gets more massive and bigger as your distance to the object gets smaller.
Now, light isn't infinitely "strong"/fast -- it has a limit.  Even the fastest runner can't run up a hill if the hill is steep enough ... against a river if the river is strong enough ... or away from a rope if the rope is tight enough.
Imagine light running away from an object with gravity.  Now make the mass bigger and bigger ... or the distance to the light smaller and smaller.  Because light isn't infinitely "strong", there has to be a point where the gravity gets strong enough -- the hill gets steep enough, the river gets strong enough, the rope gets tight enough -- that light reaches that point where it just "gives up".  Like a runner running against a river that's getting faster and faster, there's a point where the river just gets too fast.
At that point -- that too-steep, too-strong, too-tight point -- that object becomes a black hole.
And well, because light is the fastest thing there is ... if light can't outrun a black hole, nothing can.

A: I would avoid the use of the term 'singularity' and keep it short and crisp: "Any region containing a mass $M$ is believed to be a black hole, if we can rotate around it a circular hoop with circumference $L$ such that the ratio $L/M$ equals $9.331 10^{-27} m/kg$." 
The explanation could then continue with the usual remarks: 
"Black holes combine some remarkable properties. Most notably, the region circumscribed by the hoop is in a way disconnected from the universe outside. All an outside observer can learn about the region 'inside the hoop', is the mass, the angular momentum and the electrical charge it contains. No other information can leak out. Note that while the mass/circumference ratio ($M/L$) is prescribed, the mass density ($M/L^3$) can attain any value. Small black holes are incredible dense, very large black holes can be less dense than earth's atmosphere."
A: Draw two circles on a piece of paper and poke holes in both of them fold the paper to where a pencil can fit through the two holes you have created. This shows how a black hole works and it is a fun thing to do with kids who are interested in this subject, like myself. And i'm only 13 and I get it.
