I wondered and wondered what that meant ("she went broody"), until I saw it for myself. It must be hormones: our hen sat on an empty nest. She would not leave, ever. After a couple of days, we got some fertile eggs from a friend who has hens *and* a rooster. We gave those eggs to the broody hen -- actually put them under her. Incubation is generally 21 days, but you can *store* the fertile eggs for a few days, and you don't start the count until she is sitting on them and keeping them warm. While she was on the eggs, we lifted her off the nest once a day, in the afternoon, so that she could get a drink of water, eat a little, and poop. She would return to the nest in 20-30 minutes.
So my understanding is that they sit on a clutch of eggs from *other* hens in the flock. You know how they will all lay their eggs in the same nesting box? "Hmmm here's an egg or two... must be a safe place to leave *my* egg... perhaps somebody will come by and sit on these eggs... we'll all have babies... wheee!!!" So the broody hen is hatching her egg, and eggs from the rest of the flock too.
My broody hen hatched 5 chicks from a clutch of 10 eggs -- those kids are about 9 weeks old now, and integrated with the flock. They do get picked on though, and the older chickens won't let them on the roost. The broody hen has abandoned her motherly duties to a different hen now, and has rejoined the laying flock.
It's all so mysterious.