Grain was a revolution for society because it could be stored for long periods of times, therefore providing a buffer for the society against times of famine. Wheat is particularly easy to grow compared to some grains and it keeps very well. Also, wheat provides a large amount of grain per cultivated acre. I believe this is the main reason that wheat has been important to many civilizations.
As for bread, specifically, there are a couple of ways to prepare wheat. There is cream of wheat, bulgur/cracked wheat, and various kinds of breads (to name a few). I believe that the reason bread is so prevalent is the texture. It is more difficult to make than a bowl of cream of wheat, but it is also much more versatile. White flour, the most popular in western culture, produces a soft and sweet bread. Wheat flour has recently become more popular for nutrition reasons, but it still yields an astonishing varieties of bread. The texture of risen breads is one that has a lot of air incorporate into the gluten. This makes the bread seem more substantive, which is an important psychological benefit. Eating a large piece of risen bread can seem more filling than eating a similar amount of flat bread.
We have a store in Houston called Central Market with a full bakery inside. They offer at least two dozen different types of bread. This kind of versatility, combined with wheat’s ease of cultivation, storage, and transport, made wheat an ideal food for burgeoning civilization, in my opinion.
Perhaps even more interesting is the comparison of rice and corn civilizations to wheat cultures.