When you eat fat the fat then goes into your stomach and then goes through the digestion process.
Your body then uses the fat you eat for energy as it goes through digestion and whatever leftover fat your body doesn't digest at that time goes to other parts of your body for storage of the fat.
The body then uses that fat as more energy when you're hungry or when you're exercising.
That is why you can burn off fat when exercising and some of the fat if you eat too much fat can stay in your body which causes weight gain.
When you exercise to burn off the fat then the fat goes away because your body uses that fat for energy to allow you to keep moving and exercise.
Basically the fat you eat gets broken down during digestion and some of it gets used right away for energy, and the rest is stored.