In astrophotography we are often times trying to extract detail and colours of very faint deep sky objects from what looks like nothing but a brownish or yellowish night sky. As we try to do this on a single frame we are often greeted with a great amount of noise and little to no hint of the object that we are trying to capture. Since noise is random, if we stack the images we can then average it out to a smoother, cleaner image.
Below is an example of how image stacking made a huge improvement in the quality of my M51 Whirlpool Galaxy image.
Here is the image with 38 stacked frames. You can see much more colour and detail in the galaxy now.
The relationship between signal and noise boils down to the inverse square law.
There are many free stacking programs available. The one that I used for these shots is Deep Sky Stacker... http://deepskystacker.free.fr/english/index.html.
My latest M51 (2010)