Question: Why is the speed of sound given so much importance in Astrophysics? For example in gas outflow (and accretion) problems, we often calculate the sonic point (the point at which the outflow speed becomes equal to the speed of sound). Is it simply because speed of sound is a convenient number that can be used to scale down the variables, or is something deep involved?

Answer: 
For one thing the speed of sound determines the rate at which disturbances can propagate in the medium or the "cone of causality". And this characteristic scale in turn determines at what point the system becomes unstable and heads towards gravitational collapse. In cosmology this is known as the [Jeans instability](http://en.wikipedia.org/wiki/Jeans_length). The Jeans length - i.e. the characteristic scale which demarcates perturbations which will induce gravitational collapse from stable oscillations of the medium is given by:

$$ \lambda\_J = c\_s \left( \frac{\pi}{G\rho} \right)^{1/2} $$

where $c\_s$ is the speed of sound in the gas and $\rho$ is the mean density.
One thing I can think up immediately is that the speed of sound sets the point at which shocks are produced, and shocks produced by an outflow are an important source of heating of the interstellar or intercluster media.