Cornflour, or cornstarch, is extracted from maize as a powdered starch. The process of extraction involves soaking and grinding maize kernels in order to isolate the germ from the bran. When written with a space (particularly in the United States), 'corn flour' refers to finely ground whole maize kernels or cornmeal.
Cornflour is typically used as a thickening agent (such as for gravies and sauces), since it combines with liquids to form a smooth and creamy texture. It has no taste, which makes it well-suited for use in a wide range of recipes.
Cornflour or cornstarch is often likened to potato starch (often erroneously called potato flour), since both are made from starch extracts and both are used as thickening agents. Corn flour, meanwhile, tends to be used as a coating for fried foods.
Similarly distinct from potato starch, potato flour is made from whole potatoes, including their skin, and has a coarser texture than the extracted starch powder. It can be used in addition to other flours in baking.
The confusion between 'cornflour' (cornstarch) and 'corn flour' tends to be aggravated by the differing uses of these terms between American and British English recipes. The distinction between the two terms is of particular importance in the southern United States.