The abridged version of the process goes something like this: mix equal parts flour and water in a jar and wait. Take some of that pasty sludge out and discard it; stir in more flour and water, and keep waiting. After some period of time repeating this process over and over, you produce a bubbling, doughy-gooey mass that rises and falls with some predictability. Over time, this mixture contains the proper collection of yeast and bacteria that can leaven bread and bestow that distinctive tangy, creamy flavor and light texture that we know and love—it becomes a sourdough starter. In exact terms, we say a starter has fermentative power—the ability to convert sugars into products like ethanol, carbon dioxide, and organic acids.
Tim Chin provides both the short and long version associated with sourdough starters.