I would really appreciate if someone could explain.

What does a correlation function like a density density correlation function
$$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$
measure, or what does i mean as a function. 

And even more important how does it do this. If someone could explain this in general terms general functions of randomly variables it would be very helpfull.

I kow about [this question][1] but none of the answeres really describes what generally a correlation function signifies or how it does this mathematically. But this is exactly what i need to know.


  [1]: http://physics.stackexchange.com/questions/3168/why-correlation-functions