what is it that makes the bang when you burst a balloon?

The air in the balloon is under pressure; when it pops, that pressure
is suddenly released in a burst. When the burst of air pressure hits
our eardrum, it registers as a sound.

This is a brief paraphrase of a copywrited site:

http://amos.indiana.edu/library/scripts/bang.html

The explanation there is more detailed, but still short. They also
refer to popping a paper bag.

Search strategy: pop balloon sound bang

It is the sudden release of the air from a very pressure area to
atmospheric pressure. this rush cause a burst

All sound is made of very fast waves of high and low pressure which go
through the air to your ears.  In this case, the air inside the
balloon is under pressure to start with.  This means that inside the
balloon there will be more air in the same space as on the outside.
When the balloon is popped, all this extra air will very quickly move
outwards to even out the pressure.  This starts the first (high
pressure) part of the sound wave.  What happens next though, is that
the air is still moving so fast that it will go right past being at
even pressure and will flow right out creating the other (low
pressure) part of the wave.  There are many, many, smaller repetitions
of this that go on within the fraction of a second, and when the
pressure waves get to your ear, you hear it as sound.

A Very Very fast rip starts at the point of puncture by the compressed
air moluecules try to escape from the ballon to equal out with the air
outside the balloon. The sound is caused by the very fast rip and the
expanding air escaping out of the balloon.
The balloon actually creates a small sonic boom! One a hole is made in
an inflated ballon, the quick release of the balloon's entergy, or
air, causes the hole to grow at almost the speed of sound in rubber.
Since this speed is much higher than the speed of sound in air, the
hole in the balloon actually breaks the sound barrier, creating a
sonic boom.

Here is some more information on popping balloons:

http://www.balloonhq.com/faq/howpop.html

Why Do Balloons Go Bang?
The energy stored in the compressed air inside a balloon is not very
large at all. Balloons create very little overpressure, apparently on
the order of 5 or 6 mm of mercury when inflated to normal size. On
inflation, the pressure must be higher as the rubber just starts to
stretch because, from our stress equations above:
the modulus (stiffness) of the rubber is initially large, (it then
drops off, to finally get VERY large with increasing strain) the
balloon wall is initially thick, and the radius of the balloon is
small. Pressure falls rapidly as the balloon grows in size. This
follows from the stress/pressure relationship, and the stress/strain
curve for latex.

There is a well-understood differential equation applying to soap
bubbles relating surface tension, bubble shape and internal pressure.
The surface tension can be thought of as a *constant* hoop and axial
stress (NOT a function of strain, as in latex). Two soap bubbles
inflated to about the same size and connected with a pipe form a
system that is not stable. One soap bubble will always collapse and
the other will inflate. The smaller bubble size requires a higher air
pressure than the larger bubble; it tries to develop the higher
pressure by shrinking, but since the bubbles are connected by a pipe,
shrinking just forces the air into the larger bubble. As the bubble
size difference increases, so does the pressure difference generated
to drive the air flow. This speeds up the collapse of the small
bubble. Now, remember that the volume of a spherical soap bubble is
proportional to the cube of its diameter. Visually, the process
*appears* to speed up even more, because even for a constant air flow
rate through the pipe, the diameter of the small bubble will be
decreasing at a much greater rate than the large bubble diameter will
be increasing.

This can be demonstrated with balloons, but the size difference has to
be rather noticeable before the process will begin. When it does
begin, it can become rapid and it can suddenly halt. With balloons,
this is a much more complex experiment than meets the eye because
there are so many variables changing at once. The 500 - 600% strains
make it a "large deflection" problem, in which we can't make any of
the simplifying assumptions which we usually do. The geometry changes
substantially, and latex displays highly nonlinear behavior.

The sudden halt even shows up in ONE balloon when you are using 260's.
Partially inflate a 260 and what do you get? a large diameter, thin
wall, high stress bubble with 500 - 600% strain, a small diameter,
thick wall, low stress nipple with but a few % strain, and a
transition region between them. Note that each of these two distinct
sections contains the same pressure! How is this possible? It's
possible because this large deflection problem in nonlinear elasticity
(remember the sigmoidal stress-strain curve?) has more than one stable
solution! Amazing if I do say so myself!

As balloons reach maximum expansion they get to a point where the
latex runs out of stretch and gets stiff and resists further
stretching. This is obvious in a fresh, overinflated balloon. It will
become stiffer and get very rigid as all the latex molecules all
become oriented in the tensile stress directions. This increase in
stiffness will cause balloons, unlike soap bubbles, to increase in
internal air pressure just before bursting.