You can’t talk about flour without considering gluten, for two reasons: Some people can’t eat it, and some types of baking can’t happen without it.
Gluten gives people with celiac disease a variety of near-intolerable troubles, including keeping their bodies from absorbing nutrients. Some non-celiacs seem to have trouble with gluten also, for reasons that are less clear, but this isn’t the place to discuss that. Let’s just acknowledge that right now many people avoid gluten in their diets.
Gluten gives some doughs the structure needed to rise, as well as their characteristic chew. Bakers talk about a flour having low or high gluten strength, and about a dough or batter forming or developing gluten. When flour containing high amounts of gluten is mixed with water, an elastic, weblike structure is formed. It is this structure that captures the carbon dioxide bubbles produced by yeast or other leavening agents (like baking powder) while the dough rises. This structure becomes permanent — baked in, as it were — as the bread, cake, muffin, or cookie bakes and moisture evaporates, leaving behind the nooks, crannies, and air pockets we call the “crumb.”
All high-gluten flours are high-protein, but not all high-protein flours are high in gluten. Of all the grains, wheat is highest in gluten, with hard wheat containing more gluten than soft wheat. That’s why, when you want to make a traditional, crusty, open-crumbed hearty loaf of bread, bread flour is your best choice, as it is milled from 100 percent hard wheat.
But the toughness contributed by gluten is not always desirable: Think of bread that you pull with your teeth, as opposed to a delicate muffin, where a fine, tender crumb is the goal. That’s why pancake and cake and muffin batters sometimes use cake flour (which is low-protein and therefore low-gluten) and why recipes for these (and for pie doughs, biscuits, and the like) instruct you to stir or mix or otherwise handle minimally; handling develops gluten and therefore toughness in baked goods that should be just the opposite.