A mother culture is sometimes known as a starter dough and is a fermenting dough that is used to 'start' the fermentation process in the bread you are going to make by adding a bit of the starter dough to the dough you are making. Mainly sourdough I think, but I believe you can use different mothers for different breads.
The starter dough is 'fed' flour and water to keep it alive and going, and then used everyday to make the days bread. The mother can then be kept going for many years and gives the bread made using it a distinctive flavour.
At least that's my understanding, I'm hoping to get a more detailed picture from this and the answer to my question...
There is a good blog post on the Al Dente blog that talks about getting started with a sourdough starter. They use a starter from King Arthur Flour that is supposed to be 250 years old. :)