In baker's lingo, this is called "delayed-fermentation," and that is exactly what you're doing!
When dough is refrigerated, the yeast and bacteria go dormant, but the enzymes that have been breaking down flour starches into sugar keep on trucking. This gives you a much higher percentage of simple sugars in your final dough than you would otherwise. The final loaf will have sweet nutty flavors and the crust will get nicely caramelized.
Right after you shape the loaf, cover it with plastic wrap and put it in your fridge where it won't get bumped or jostled. The next morning, set it out on the counter and let it continue rising. Since it has to come up to room temperature first, it will take longer than normal for the loaf to be ready to bake. Allow for double the time estimated in the recipe for the final rising, and then bake as directed.
Since wild yeast is so hardy and long-lived, this technique works particularly well with sourdough breads. But give it a try with your next loaf of regular bread and you'll definitely notice a difference in your final loaf!
(Image: "Bread is Baked" by Peter Seal, $7.99 via AllPosters.com)