Bread flour is a higher protein flour made from hard wheat. The protein produces gluten when made into a dough. The higher gluten dough produces a different bread texture, it's more chewy and 'tougher' in texture.
Cake flour is a lower protein flour made from soft wheat. The lower protein produces less gluten resulting in lighter, softer baked goods.
As bethzaring explained, AP flour is a blend of hard/high protein and soft/low protein flours that provides a compromise flour that works in a lot of different recipes.
You can make cake with AP flour that will not be as light as a cake made with cake flour and you can make bread with AP flour that won't be as chewy as bread make with bread flour.