Bread is made out of flour that comes from grain kernels — usually wheat. A grain kernel has three parts: the bran, the endosperm, and the germ (so called because it's the part of the kernel that germinates into a new plant).
Whole grains contain all parts of the grain kernel. But refined grains, like the flour used to make white bread, have had the fiber-dense bran and the nutrient-rich germ processed out, leaving only the starchy endosperm. This means that refined grain is not as rich in essential fatty acids, vitamin E, magnesium, and zinc.
Some flour and bread manufacturers "enrich" their bread by adding extra vitamins back in. But it's still better to eat whole grains. The fiber and protein from the bran and germ provide a more constant source of energy, which will keep you going long after the energy from refined grains is gone. The fiber in the bran can also mean whole-grain breads help people feel full longer, preventing overeating. If you're buying packaged bread in the supermarket, be sure the label says "whole grain" or "whole wheat."