A preferment is a portion of the recipe prepared in advance of the main mixing session. It can be as simple as a piece of dough reserved from a previous bake and stored on the counter or in the refrigerator, or as complex as as three-day build of a biga or poolish. There are four main preferments in use these days.
Old Dough is merely a piece of the previous batch of dough that has been reserved to be used as a flavoring enhancer for a new batch of dough.
Biga is an Italian stiff preferment, usually around 60% hydration, although some recipes make it as high as 100% hydration, which would make it a poolish, but they call it a biga. Whatever it’s called, it is the preferred preferment for very long development, since there is enough nutrient to carry the yeast.
Poolishis a French preferment, usually made around 100% hydration. The name derives, so the story goes, from the Polish bakers who exported the recipe to Vienna, where the French found it. True or not, it’s a nice story.
Sponge seems to be mostly used in the British Isles. It’s a short-time preferment, usually made with all the water, salt and yeast and half the flour. I use it when I’m making a straight dough recipe and have a bit of extra time, like an hour.
Whatever you call them and where ever they come from, preferments will make your bread better if you use them. Check out the recipes for them and then note where I use them in the main bread recipes. You can switch from a biga to a poolish to a sponge for just about any recipe, just be sure to take into account the amounts of flour, water and yeast in the preferment when you calculate how much to add to them to make the final dough.