A sourdough starter is what bakers call a pre-ferment. It is a small amount of flour and water that has been left to ferment until it is full of wild yeasts and lactic acid bacteria. When you mix that lively starter into a bigger dough, it carries the fermentation along with it.

Commercial yeast is a single strain of yeast, grown and packaged for consistency. It works quickly, which is why a yeasted loaf can be made in a few hours. A sourdough starter is a community of yeasts and bacteria, which is why it takes longer but also gives a more complex flavour and a different texture.

If you would like to read more about the history and science of sourdough, the Wikipedia article on sourdough is a good place to start.