The main ingredient of bread dough is flour. This is mostly starch, but also contains proteins, known as gluten. We know that the gluten is crucial for bread-making quality, as it helps make the dough stretchy and elastic. On the small scale, dough is mixed and must then be kneaded. The physical and biological changes caused by kneading are not fully understood, but they seem to make the dough more elastic.
Air also seems to be crucial to the process.
If the dough is kneaded in an atmosphere containing, say, nitrogen instead of air, the resulting loaf is of poorer quality. In baking, yeast is added to the dough and produces a gas - carbon dioxide, which makes the loaf rise. Leaving the dough to 'prove' allows the gas bubbles produced by the yeast to expand. So bread dough is really just a 'foam' - a collection of bubbles. This is where the gluten plays a crucial role.