Why do the queen ant and the queen termite have large abdomens?

Answer 1

Queen ants and queen termites are the ones that must lay eggs; the workers of most kinds either cannot lay eggs, or are not allowed to; that is the queen's job. In most species queens have to lay not only enough eggs to produce workers to get food, build the nest, feed the young and the queen or queens, but also to produce the young that go out to start up new colonies of ants or termites. In fact in most species the queens have to lay enough eggs for every member of the whole colony that cannot lay their own.

On the other hand, in most species the queens don't have to do anything else; the workers do the rest. But the eggs the queens must lay don't come from nowhere; they have to be made by a special body part called an ovary (meaning roughly: egg-thing, egg-making-place, eggery or something like that). Every breeding female has ovaries; in the case of most ant and termite queens, she hardly needs anything else but she does need huge ovaries for the huge numbers of eggs she must lay. The ovaries of an insect are in the abdomen, so the queen's abdomen has to be large, often weighing hundreds of times more than the rest of the queen's body.

Which was what you asked.