It is rather simple; if you use smaller plates you take smaller portions.
By having smaller portions, you eat less. By becoming accustomed to eating less, you are not hungry.
It is, of course, a way to prevent obesity, a way to avoid wastage. It is also a way to savour each bite, and save money.
Using those large dinner plates, which encourages heaping of food and the imposition of having to clean your plate is unwise.