Bleached flour is wheat flour that has had a chemical whitening agent added to it. The whitening process gives the flour a lighter color and a softer texture than unbleached flour, but it does not have much of an impact on the flavor of the flour when compared to unbleached all purpose flour. In addition to lightening the color, bleaching also lowers the protein content of the flour, which means that baked goods made using it will be slightly more tender. Most cake flour, unless it states otherwise on the packaging is bleached, as the soft texture and low protein content are the defining features of cake flour.
There are two main reasons to use bleached flour over unbleached flour: when you want baked goods that are exceptionally white or when you need a softer texture in your baked goods. Recipes like angel food cakes and pound cakes can sometimes call specifically for bleached flour because of this, just like recipes that use cake flour over all purpose. If you encounter a recipe that calls specifically for bleached flour, you may end up with a slightly denser finished product if you substitute unbleached flour into it. You will be more likely to see the difference in delicate cakes than in drop cookies and bar cookies.