@weaseleyes re fat cells. In general, the actual fat cells don't disappear, they just lie 'empty'.
I once heard it described as like an investment bank. If you liken the energy your body needs moment-to-moment, day-to-day to money, then glucose (in your blood stream) and glycogen (in you muscles, liver etc) are like the cash in your purse. If you need to pay for something you use that first. Once that is all used up, you have to go to 'the bank' - your fat cells - where your long-term deposits are held.
For us, we are still using our 'cash' when it's available but as we are eating less, and particularly less sugar and easily accessible carbs, the cash is gone more quickly and we are taking fat out of the bank. (Hurrah!) The fat cells are then like a dormant bank account, we are not using them but they remain in existence. Then if there is a 'lottery win' (aka an enormous pizza with cheese and sausage stuffed crust, followed by double caramel toffee pudding and a heap of alcohol), our cells can easily bank the excess energy without having to go to all the unnecessary trouble of opening a new account!
It is the amazing phenomena of bodies developed when we were hunter gathers - using the energy available and being able to store it when there was excess food. Add to that the wonder of insulin, so if we came across a honeycomb we could gorge ourselves on sugar and still survive. However, our ancestors might find honey once or twice a year, not every time they stopped to get petrol or bought a coffee. That is the long term challenge for many of us. When I get to goal weight, how do I maintain it? Will I have changed my eating habits, will I have learned tricks and techniques that work for me? Who knows. But we're all doing so well to be making this progress. That's the focus for now.