What is a a colour-space?
Scientifically it is a abstract mathematical model describing the way colors can be represented. What this means is that any particular colour-space has a limited number of colours it can contain. So photographically we often hear about the sRGB colour-space. What this actually is, is a formula for displaying and representing all the colours that the sRGB colour-space is able to use.
Not all colour-spaces are equal, some contain the ability to display/use more colours than others.
Here is a small chart representing some of the more commonly used colour-spaces
Illustration courtesy Jeff Schewe
from A Color Managed Workflow
which is found on the Adobe Web site.
As can be seen in the graphic above, some colour-spaces contain a larger range of colours than others. This can be important as far as we photographers are concerned cause we work everyday with colours. When you compare the sRGB colour-space to the ProPhoto colour-space, you can see how many colours are being 'clipped' when you photograph or process using sRGB.
I hope this small post gives you an early insight into colour-spaces and how they can affect the results you see when you take photos.