Flour and other starchy substances have a number of uses in the kitchen, primarily in baking and for thickening sauces or other liquids. Wheat flour has been an important ingredient and thickener for centuries, because of its wide availability. Refined starches such as cornstarch, and less-common alternatives including tapioca, are more recent arrivals in the pantry. All thickeners work in much the same way, but there are functional differences between flour and other starches, such as tapioca.
How Starches Thicken
Most plants contain starches in varying concentrations, with grains, root vegetables and some beans having especially large amounts. They're usually stored in the plant in the form of fine, tightly wound granules. If they're dispersed in water and heated, those granules absorb water and begin to swell. When they reach a specific temperature -- different for each starch -- they burst open, and the molecules of starch lose their compact shape. Instead they bond together in a large, open mesh, trapping and immobilizing the liquids to form a soft gel.
Thickening with Flour
White wheat flour is made by separating the fibrous bran and oily germ from the wheat kernel, then grinding the remainder. Wheat flour is approximately 75 percent starch, along with the gluten-forming proteins that make bread possible and a few other substances. Because it's not pure starch, flour takes longer to absorb water and create a thickening gel. Cooks must also use more flour to thicken any given volume of liquid. Some manufacturers sell "quick-mixing" or "instant" flour, which has been heated to a gel and then dried and re-ground to a fine powder. This pre-cooking means it thickens sauces almost instantly, much like tapioca or cornstarch.
Tapioca is a very different starch, derived from a widely grown tropical root called manioc or cassava. It's a powerful thickener that develops long strands of starch, which are highly effective at immobilizing liquids. Unfortunately it also tends to give sauces a disconcertingly stringy texture. It's usually formed into small beads, or "pearls," which thicken puddings by absorbing liquid and becoming soft much as pasta does. The pearls also release a small amount of starch into the surrounding liquid, creating a creamy sauce in much the same way as risotto rice.
There are a number of practical differences in how these starches are used. Flour gives a distinct flavor and body to sauces, turning them opaque and making them rich and hearty. It holds up well under prolonged cooking, making it suitable for stews and similar dishes that are kept hot. Tapioca has a perfectly neutral flavor and creates a clear sauce, which is often desirable. It quickly loses its thickening power under continued heat, so it's most often used in desserts and other applications where it will be chilled. It reaches its full thickening power at 150 degrees Fahrenheit as opposed to flour's 185 F, so it's also better suited to fresh fruit fillings and sauces that benefit from minimal cooking.
The other major use for flour and tapioca starch is in baking. Wheat flour is the most common choice for general-purpose baking because of its relatively neutral flavor and its ability to form gluten chains, which provide most baked goods with their structure. Other flours such as buckwheat and oat flour are valued for their flavors, but less widely used. The exception is in gluten-free baking, where wheat is excluded by default. Most commercial and homemade gluten-free flour mixtures include tapioca starch, because its characteristic of gelling at low temperatures helps provide some structure to baked goods in the absence of gluten.