The fat is "burned" (like in a petrol engine) turned into kinetic energy (moving your body - also like in a car), heat energy (keeping your body at 37C takes energy), protein cells from your food are used to repair organs, and the "exhaust" is everything you excrete, eg CO2, heat, urea and a part of poop and some water
So if you imagine a gram of fat is like a gram of coal - a single solitary chunk. That coal gets burned/used up and the exhaust of that coal is water, CO2, and some noxious stuff. After all the fuel is burnt out of the coal, then you are left with charcoal - another solid by-product of the burning/using up process.
I think it's probably best to think about it in the "fat is reserve fuel" way. It's probably the best analogy
So the "matter" in this case fat, changes form (in the form of CO2, water and urea and other gunk) oh and also some of the matter turns into body cells (did you know that in a year, none of the cells that are make YOU right now will exist?) - so yes mass does still exist in the world somewhere, in the atmosphere as excreted gases and in the sewers as excreted solids.
