Why would the people of Ember have beehives?

Because of their city's subterranean location, the people of Ember are pretty limited in what kind of food they can produce. They can't raise animals for their meat as they don't have enough of a food surplus to share with them; there's not enough food to go round for the humans, let alone any animals. As for growing fruit and vegetables, well that's becoming increasingly difficult. There's no natural sunlight, and so the greenhouses used for growing plants need to rely on the malfunctioning power supply to nourish the soil. To make matters worse, supplies of canned food are starting to run out, which means that the unfortunate people of Ember are left with little choice but to keep bees for their honey.