Many times you will want to thicken a sauce, soup, custard or gravy and either cannot or do not want to use flour. Clearly something like a custard would have a strange texture and flavor if it was thickened with flour.
If the liquid you want to thicken is hot then you would form a slurry in cold water, and then transfer that slurry into the soup or stew.
1 tablespoon of cornstarch is about equal to 2 tablespoons of flour. If a recipes calls for flour, use one half as much cornstarch. Place cornstarch in some water and make a paste.
Ex. 1 tablespoon cornstarch mixed with 1 ounce of water. Whisk thoroughly and mix into your soup or stew.
Note: You form a roux with flour and fat, not cornstarch and fat.