In order to burn fat for water, you must be able to break down fat (lipolysis). Elevated insulin levels inhibit lipolysis.
What that means is that when you eat, and for a while after you eat, you won’t be breaking down fat (for energy or water).
So if you’re just eating your normal diet but not drinking enough fluids, you will become dehydrated (you will sweat, pee and exhale too much of the water that you need for all kinds of bodily functions).
But if you’re fasting, and your insulin levels are low enough, and you have enough extra body fat, then you can make some of the water you need by breaking down fat.
Fat and glucose are chains of carbon atoms with hydrogen atoms. The air contains oxygen atoms. The metabolic process of breaking down fat and glucose frees up the hydrogen atoms from the chains of atoms of fat and glucose, and those now-free hydrogen atoms can bond with the oxygen atoms in the air to form H2O, water.