There are a number of different mechanisms that green vegetables aids your body, and therefore helps it lose fat.
Number one is that they contain a lot of fibre. Fibre will help minimize the amount of insulin you secrete.
Insulin is related to fat gain or fat loss. So by having larger amounts of fibre, your blood sugar will be more stable and you are far less likely to crave sugars.
Another great reason for you to eat your veg is it helps your body detoxify.
If you don't detoxify, you're going to store more body fat. The compounds within green vegetables are natural detoxifiers and are very important in helping your body to get rid of any chemicals or pesticides that it takes in.
They do actually say that one of the main reasons we're more overweight now in the modern day is because of lack of excretion of toxins. Therefore taking large amounts of toxins in is one of the reasons peple store body fat.